Sachin Physics Revision Topic 1: Physics and Physical Measurement: The realm of physics: The order of magnitude is i.e. 10 x . Range of masses (kg): 10 -32 (electron) to 10 52 (mass of the observable universe) Range of lengths (m): 10 -15 (diameter of proton) to 10 26 (radius of universe) Range of times (s): 10 -23 (passage of light across a nucleus to 10 19 (age of the universe) Measurement and uncertainties: Fundamental units: Quantity SI unit SI symbol Mass Kilograms Kg Length Meters m Time Seconds s Electric Current Ampere A Amount of Substance Mole mol Temperature Kelvin K Derived units are different combination of the fundamental units For example speed = distance/time = meters/seconds =m/s =ms -1 Remember to state answers in the format ms -1 Important Prefixes: Giga G 10 9 mega M 10 6 kilo k 10 3 centi c 10 -2 milli m 10 -3 micro µ 10 -6 nano n 10 -9 pico p 10 -12
Transcript
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Physics Revision
Topic 1: Physics and Physical Measurement:
The realm of physics: The order of magnitude is i.e. 10x. Range of masses (kg): 10-32 (electron) to 1052 (mass of the observable universe)Range of lengths (m): 10-15 (diameter of proton) to 1026 (radius of universe)Range of times (s): 10-23 (passage of light across a nucleus to 1019 (age of the universe)
Measurement and uncertainties: Fundamental units:
Quantity SI unit SI symbolMass Kilograms Kg
Length Meters mTime Seconds s
Electric Current Ampere AAmount of Substance Mole mol
Temperature Kelvin K
Derived units are different combination of the fundamental units
For example speed = distance/time = meters/seconds =m/s =ms-1
Remember to state answers in the format ms-1
Important Prefixes:
Giga G 109
mega M 106
kilo k 103
centi c 10-2
milli m 10-3
micro µ 10-6
nano n 10-9
pico p 10-12
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Random errors are errors in measurement caused by different factors
Random errors include the readability of the instrument and the effects of a change in surroundings. Repeated readings do reduce random errors.
Systematic errors are errors due to faulty equipment/calibration.
Systematic errors include an instrument being wrongly calibrated. Repeated readings do not reduce systematic errors.
Individual measurements: the error is ± the smallest value e.g. .5mm
When we take repeated measurements and find an average, we can find the uncertainty by finding the difference between the average and the measurement that is furthest from the average.
A precise experiment is one with a small random error, i.e. the more significant figures the more precise.
An accurate experiment is one with a small systematic error, i.e. the nearer the real value the more accurate.
Give answers to the same amount of significant figures as the least precise value used.
If you have the measurement for a football pitch of 100m±1m
The absolute uncertainty is 1m
The fractional uncertainty is 1/100 = .01
The percentage uncertainty is .01 x 100 = 1%
For addition and subtraction, the absolute uncertainties can be added
When 2 quantities are multiplied or divided the overall uncertainty is equal to the addition of the percentage uncertainties
Powers = # of power x uncertainty.
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For other functions such as trigonometric function, the mean, highest and lowest answers may be calculated to obtain the uncertainty range.
Uncertainties in graphs: Error bars. Note that a line of best fit should pass through all error bars. Some easy ways to get round this are just to plot the first and last value of error bars or just the worst value and assume the same for all.
Uncertainty in slopes is shown by max and min gradients using the first and last gradients
The same can be done for the uncertainty in intercepts.
1.3 Vectors and Scalars:
A vector has magnitude and direction. A scalar only has magnitude. E.g. all forces are vectors.
Proportional is a straight-line that passes through the origin.
Gradients units are the y-axis/x-axis i.e. rise/run. Only if the x-axis is a measurement of time des the gradient represent the rate at which the quantity on the y-axis increases.
Area under a straight-line graph is y-axis x x-axis.
Topic 2: Mechanics:
2.1 Kinematics:
Displacement is a vector quantity and is the distance moved in a particular direction
Velocity is a vector quantity and is the rate of change of displacement
Speed is a scalar quantity and is the rate of change of distance
Acceleration is a vector quantity and is the rate of change of velocity
Average velocity is the change in displacement divided by the change in time.
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Instantaneous velocity is the change in displacement as the change in time becomes infinitely small.
Speed and acceleration work in the same way
Equations for uniformly accelerated motion can only be used when the acceleration is constant, i.e. uniformly accelerating in the same distance.
Equations of uniform motion:
u = initial velocity
v = final velocity
a = acceleration
t = time
s = distance
v=ut+at
s=(u+v/2)t
v2=u2+2as
s=ut+.5at2
In absence of air resistance, all falling objects have the same acceleration of free-fall, independent of their mass, 9.8 ms-2
When the drag force reaches the magnitude of the force providing the acceleration, the falling object will stop accelerating and fall at a constant velocity. This is called the terminal velocity
Relative velocity is determined by frames of reference i.e. if one car is at 20 and another is at 25, then from the first car the other car looks to be going at 5.
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Additional: Ways to record the motion of velocity/acceleration: light gate, strobe photography, ticker timer.
2.2 Forces and Dynamics:
Weight = mg
Forces include: gravitational force, friction, tension, the normal force, etc
In a free-body diagram only one object is chosen and all the forces and shown and labelled.
Newton’s first law of motion states that an object continues in uniform motion in a straight line or at rest unless acted upon by a resultant external force. The law of inertia.
An example of this is a ball rolling on a frictionless surface will roll forever unless an external force acts on it.
The condition for translational equilibrium is that the net force on an object is zero.
Objects in equilibrium must either be constantly at rest or moving with constant velocity. Static equilibrium would be a book on a table. Dynamic equilibrium would be a book being dragged across a table at a constant speed.
F=ma. The net force acting on an object is the product of the objects' mass and the net acceleration of the object.
Linear momentum is the product of mass and velocity. P=mv. It is measured in kg ms-1.
Impulse in the change in momentum (I=Ft). Impulse also equals (p’ –p) Ft=mv
The impulse of a time-varying force is represented by the net area under the function (the integral) of the force-time graph.
Law of conservation of momentum: The total momentum of a system remains constant provided there is no resultant external force.
Newton’s third law states that when a force acts on a body, an equal and opposite force acts on another body somewhere in the universe.
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One example would be two roller-skater’s pushing off one-another
Additional:
Mass is the amount of matter contained in an object measured in kg, whilst weight is a force measured in N.
2.3 Work, energy and power:
Work done = Fs cosΘ.
The amount of energy transferred is equal to the amount of work done
If the force and displacement are in the same direction then Work done = Fs
Work is measured in N m = Joules.
The area below a Force-displacement graph is equal to the work done.
Work done in compressing or extending a spring = .5 kx2
Gravitational potential energy = mgh
Kinetic energy is the energy a body possesses due to motion. =.5mv2
Principle of conservation of energy: Energy cannot be created or destroyed, it just changes form.
0.5mv2=mgh
There are many different forms of energy.
Thermal energy includes the kinetic energy of atoms and molecules.
Chemical energy is the energy that is associated with the electronic structure of atoms and is therefore associated with the electromagnetic force. An example where chemical energy is converted into kinetic (thermal) energy is the combustion of carbon. Carbon combines with oxygen to release thermal energy along with light and sound energy.
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Nuclear energy is the energy that is associated with the nuclear structure of atoms and is therefore associated with the strong force. An example is the splitting of uranium nuclei by neutrons to produce energy.
Electrical energy is associated with electric current. Boiling water can turn a turbine with a magnet which rotates in a coil to induce electrical energy.
An elastic collision is when there is no mechanical energy that is lost. In other words, the total kinetic energy of the objects is the same before and after the collision. An inelastic collision is where mechanical energy is lost. Almost always in reality collisions are inelastic as energy is lost as sound and friction.
Power is the rate at which energy is transferred or which work is done.
Power = work done/time or energy transferred/time.
Power = force x velocity
Efficiency is the ratio of useful energy to the total energy transferred.
Efficiency = useful/total
Uniform Circular Motion: An object going round a circle at constant speed
For an object to move around in a circle, it must be travelling in a direction at the tangent to the circle where the object is at, and direction of the force being applied must be perpendicular to the direction the object is travelling in. The direction of the force is pointing to the centre of the circle
The acceleration of a particle travelling in a circular motion is centripetal acceleration
The force needed to cause the centripetal acceleration is called the centripetal force.
Centripetal force does not do any work as work done = force x distance in the direction of the force.
Examples of forces which provide centripetal forces are gravitational forces (planets orbiting in a circle), frictional forces (car driving in circles), magnetic forces or tension (string). F=ma. a = v^2/r. Therefore, F=mv^2/r
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Topic 3 Thermal Physics:
Temperature is a scalar quantity that gives indication of the degree of hotness or coldness of a body.
Temperature determines the direction of thermal energy transfer between two bodies in contact; from the body at higher temperature to the body at lower temperature.
Thermal equilibrium occurs when all parts of the system are at the same temperature. There is no exchange of heat.
T(Kelvin) = T(Celsius) +273. They have different zero points.
Internal energy of a substance is the total kinetic and potential energy that molecules possess. They have kinetic energy from their random/translational/rotational movement and potential energy from the intermolecular forces.
Temperature is a measure of the average kinetic energy of the molecules in a substance.
A mole is the basic SI unit for amount of substance. One mole of any substance equals the same number of atoms as 12 grams of carbon.
Molar mass is the mass of one mole of substance. If an element has mass number A, then the molar mass will be A grams.
Avogadro’s constant is the number of atoms in 12 g of carbon-12. It is 6.02 x1023.
3.2 Thermal properties of matter:
Thermal capacity (C) is the energy required to raise an object’s temperature by 1K. C=Q/ΔT
Specific heat capacity is the energy required to raise a unit mass of substance by 1K. c=Q/(mΔT)
The difference is that thermal capacity measures the substance’s ability to absorb heat as an entire object, whereas specific heat capacity measures the substance’s ability to absorb heat per unit mass.
If an object is raised above room temperature it starts to lose energy. The hotter it becomes the greater rate at which it loses energy.
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Molecules are arranged in different ways depending on the phase of the substance, (i.e. solid, liquid or gas)
Solids: Fixed volume and fixed shape. The molecules vibrate about a fixed position. The higher the temperature the greater the vibrations.
Liquids: Fixed volume but shape can change. Molecules are vibrating but not completely fixed in position, still strong forces between molecules.
Gases: Not fixed volume or shape, will expand to fill the container. Forces between molecules are weak. Molecules are essentially independent but will occasionally collide.
While melting, vibrational kinetic energy increases and particles gain enough thermal energy to break from fixed positions. Potential energy of system increases
• While freezing, particles lose potential energy until thermal energy of the system is unable to support distance between particles and is overcome by the attraction force between them. Kinetic energy changes form from vibrational, rotational and part translational to merely vibrational. Potential energy decreases.
• While evaporating, certain particles in the liquid gain enough potential energy to escape the intermolecular bonds as a gas. The escape of the higher-energy particles will lower the average kinetic energy and thus lower the temperature.
• While boiling, substance gains enough potential energy to break free from inter-particle forces. Similar to evaporation, the only difference being that energy is supplied from external source so there is no decrease in temperature
When condensing it’s the opposite of boiling.
During a phase change, the thermal energy gained or lost will go towards increasing or decreasing the potential energy of the particles to either overcome or succumb to the inter-molecular force that pulls particles together. In the process, the average kinetic energy will not change.
The energy given to molecules does not increase kinetic energy so it must increase potential energy. Intermolecular bonds are broken are being broken and this takes energy. When a substance freezes, bonds are created and this releases energy. Molecules do not
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speed up during a phase change.
Evaporation differs from boiling as evaporation is a change from the liquid state to the gaseous state that occurs at a temperature below the boiling point.
Specific latent heat is the amount of energy per unit mass absorbed or released during a change of phase. Specific latent heat (L). L=Q/m
Fusion: The change of phase from solid to liquid
Vaporization: The change of phase from liquid to gas
Pressure is the force gas molecules exert due to their collisions (with an object). P=F/A i.e. force per unit area.
Assumptions of the kinetic model of an ideal gas:
Newton’s laws apply to molecular behaviour
There are no intermolecular forces
The molecules are treated as points
The molecules are in random motion
The collisions between molecules are elastic
There is no time spent in these collisions.
Decrease in volume results in a smaller space for gas particles to move, and thus a greater frequency of collisions. This results in an increase in pressure.
PV/T = PV/T
Topic 4 Oscillations and Waves:
Examples of oscillations include the swinging of a pendulum
Displacement (x) is the instantaneous distance of the moving object from its mean position
Amplitude (A) is the maximum displacement from the mean position
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Frequency (f) is the number of oscillations completed per unit time. Measured in Hertz (Hz)
Period (T) is the time taken for one complete oscillation. T=1/f
Phase difference is a measure of how “instep” different particles are. If they are 180 degrees or (pi) off, they are completely out of phase by half a cycle.
Simple Harmonic Motion (SHM) is motion that takes place when the acceleration of an object is always directed towards and is proportional to its displacement from a fixed point.
This acceleration is caused by a restoring force that must always be pointed towards the mean position and also proportional to the displacement from the mean position.
a=-w2x where w is the angular frequency and is a constant. The negative sign signifies that acceleration is always pointing back towards the mean position.
4.1.5 p 34 4.1.6
4.2 Energy changes during simple harmonic motion (SHM):
During SHM energy is interchanged between KE and PE
If there are no resistive forces then energy remains constant and the oscillation is said to be undamped.
Ek=.5mv2=.5mw2(A2-x2)
Ep=.5mw2x2
Total energy, Et=Ek+Ep=1/2mw2A2
4.3 Forced Oscillations and Resonance:
Damping involves a frictional/dissipative force that is always in the opposite direction to the direction of motion of the oscillating particle.
As the particle oscillates it does work against this force and loses energy
Underdamping: The resistive force is so small that a small fraction of energy is removed every cycle. Time taken for oscillations to die out can be long
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Overdamping: involves large resistive forces and can completely prevent oscillation from taking place. Again the time taken for the particle to return to zero displacement may be long.
Critical damping: Involves an intermediate value of resistive force such that the time taken for the particle to return to zero displacement is at a minimum. Effectively there is no “overshoot”. Example: door closing mechanism.
If the system is temporarily displaced from the equilibrium position the system will oscillate. The oscillation will be at the natural frequency of vibration of the system.
Forced oscillations when an external force is applied on a free system with a frequency f , the system may respond by switching to oscillations with a frequency equal to the driving frequency f0
For a small degree of damping, the peak of the curve occurs at the natural frequency of the system.
The lower the degree of damping, the higher and narrower the curve.
As the amount of damping increases, the peak shifts to lower frequencies.
At very low frequencies, the amplitude is essentially constant.
Resonance occurs when a system is subject to an oscillating force at exactly the same frequency as the natural frequency of oscillation of the system.
Where resonance is useful: microwave oven, radio.
Where resonance is harmful: bridges, aeroplane wings.
4.4 Wave Characteristics:
Waves:
Transfer energy from one place to another without a net motion of the medium in which they travel
Involve oscillations in SHM
A continuous wave involves a succession of individual oscillations
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A wave pulse involves just one oscillation
Transverse waves are waves where the oscillations are at right angles to the direction of energy transfer, such as light waves and water waves. Transverse waves cannot propagate in a gas.
Longitudinal waves are waves where the oscillations are parallel to the direction of energy transfer such as sound waves
The wavefronts highlight the part of the wave that are moving together
The rays highlight the direction of energy transfer
A crest is the top of the wave
A trough is the bottom of a wave
A compression is a point on the wave where there is high pressure (everything is bunched up)
A rarefaction is a point on the wave where there is low pressure (everything is far apart)
Displacement is the amount by which a particle has moved from its equilibrium position
Amplitude is the maximum displacement from the mean position
Period is the time taken in seconds for one complete oscillation
Frequency is the number of oscillations that take place in a second.
Wavelength is the shortest distance along the wave between two points that are in phase
Wave speed is the speed at which wave fronts pass a stationary observer
Intensity is the power per unit area that is received by the observer. The intensity of a wave is proportional to the square of its amplitude.
4.4.7: Graphs p39
Velocity = distance/time = wavelength/period. Since frequency = 1/period
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Velocity = Frequency x Period
Waves that carry various types of light are electromagnetic waves and they travel at the speed 3x108ms-1
Wave Properties:
In general when any wave reaches the boundary between two different media it is partially reflected and partially transmitted. P41
The law of reflection: when a wave is reflected, the angle of incidence equals the angle of reflection and the incident ray, the normal line, and the reflected ray line in one plane.
Reflection (fixed end): when a pulse of a string attached to a support hits the wall it is attached to, it is reflected—inverted with the same shape (undergone a 180 – degree change in phase).
Reflection (free end): like above, the pulse comes back but without being inverted
Snells Law states that sin i/sin r = constant for a given frequency
sin I / sin r =v1/v2
Diffraction refers to the spreading around of waves about obstacles or when passing through apertures.
Examples of diffraction are:
Why we can hear something even if we cannot see it
The principle of superposition: The effect of two separate causes is equal to the sum of the separate causes.
Constructive interference occurs when two waves are in phase with eachother. The resultant displacement is the sum of both displacements.
Destructive interference occurs when two waves are out of phase. The resultant displacement is the difference of both displacements.
Read more on p42-44
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Topic 5: Electric Currents:
The potential difference is defined as the work done per unit charge to move a positive test charge between A and B.
Potential Difference = Energy Difference/ Charge
The base unit for potential difference is the Joule per Coulomb (JC-1).
Change in potential energy = force x distance = Eqd
Electric potential energy is the energy a charge has as a result of its position in an electric field
Change in EPE =(change in V) x q = (Vq)
An electronvolt is the energy y gained by an electron moving through a potential difference of 1 volt.
Electric current is the rate at which charge flows past a given cross-section. I=Q/t
It can also be defined in terms of the force per unit length between parallel current carrying conductors.
Resistance is the measure of how easily current flows. R=V/I, where V is the potential voltage across an object and I is the current passing through the object
R=pl/A where p is the resistivity of the resistor, l is length and A is cross section
Ohms Law states that the current flowing through a metal is proportional to the potential difference across it providing the temperature remains constant. V=IR
If current and potential difference are proportional then the device is ohmic.
If they are not like in a filament lamp they are non-ohmic.
Power Dissipation:
Power = Energy difference/time = E/t
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E/t = VI. P=VI
Since V = IR then P=I2R and V2/R
5.2: Electric Currents:
Electromotive force (emf) is the total energy difference per unit charge around a circuit.
Internal resistance is the resistance of a voltage source such as a battery
Draw Circuit Diagrams
Describe the use of ideal ammeters and ideal voltmeters:
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Ammeters are used to measure the current in a circuit. They are connected in series with the component under test. In order to have no effect on the circuit they should have a very small resistance. Ideal ammeters have zero resistance. This means that no potential difference is dropped across them.
Voltmeters are used to measure the voltage in the circuit. They are connected in parallel with the component under test. Voltmeters have a very high resistance so that very little current is allowed to flow through them. An ideal voltmeter has an infinite resistance.
A potential divider is an electric circuit with a cell and two resistors in series. It is called so because the resistors divide up the potential difference of the battery.
A light dependent resistor (LDR) is a device whose resistance depends on the amount of light shining on its surface. An increase in light causes a decrease in resistance.
A thermistor is a resistor whose value of resistance depends on its temperature. An increase in temperature causes a decrease in resistance.
SOLVE CIRCUITS
Topic 6: Fields and Forces:
Newton’s Law of Gravitation states that every mass in the Universe attracts all other masses in the Universe given by F=Gm1m2/r2
Gravitational field strength is the gravitational force exerted per unit mass. g=F/m, g=GM/r2
6.2: Electric force and field:
There are two types of electric charge: positive and negative.
The Law of Conservation of Charge: In a closed system, the amount of charge is constant
Conductors:
A material that allows the flow of charge
All metals
Insulators:
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A material which charge cannot flow through
Plastics
Rubber
Glass
Note: There are no perfect insulators
Coulomb’s Law: The electric force between two point charges is proportional to the product of their charges and inversely proportional to the square of the distance between them
F=kq1q2/r2
Electric field strength at a point is the force felt by one unit test charge in an electric field.
Determine the electric field strength: E=F/q2=kq/r2
Electric Field Drawings p53
6.3 Magnetic Force and Field
Moving charges give rise to a magnetic field, (either magnets or electric currents)
Draw Magnetic Fields p54
When a current-carrying wire is placed in a magnetic field the magnetic interaction between the two results in a force. The direction of the force is perpendicular to the plane that contains the field and the current. P55
Magnitude force on a current: Magnitude of the electric field: (B) = F/ILsin(O)
I=Current
L=Length of Current
Sin (O) = sin of the angle between the field and current
F=BIL sin (O) where F is in (T) for tesla.
Magnetic Force on a Moving Charge:
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F=Bqv
B=magnitude of magnetic field
Q= magnitude of charge
V=velocity of charge
=Circular motion
Topic 7: Atomic and Nuclear Physics:
The atom
Rutherford Model of the atom: the atom consists of a small dense positive nucleus, surrounded by electrons that orbit the nucleus (as planets orbit the sun) as result of electrostatic attraction between the electrons and the nucleus.
Evidence supporting the nuclear model of the atom:
Geiger-Marsden Experiment:
Alpha particles were fired at a golf-leaf. Due to the size and velocity of the particles most were expected to travel straight through. However some alpha particles were deflected through huge angles caused partly by a dense, positive nucleus
One limitation of the simple model of the nuclear atom:
Did not explain why electrons surrounding the nucleus were not drawn into the nucleus by strong electrostatic attractions to the protons of the nucleus.
Did not specify composition of nucleus.
How did protons in the nucleus stay closely bound when electrostatic forces should have forced them apart?
Emission Spectra: the spectrum of light emitted by an element
Absorption Spectra: a bright continuous spectrum covering the full range of visible colors, with dark lines where the element absorbs light
Evidence for the existence of atomic energy levels:
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The emission spectra of each element is unique as electrons can only occupy specific energy levels.
Movement between energy levels requires electron to emit or absorb energy. Energy emitted or absorbed is in the form of packets of light called photons. E=hf (Energy of a photon = Planck’s constant*frequency of light in Hz). Energy is "quantized".
Nuclide: a particular type of atom whose nucleus have a certain number of protons and neutrons
Isotope: different forms of the same element that contain the same amount of protons but different amount of neutrons
Nucleon: A proton or a neutron
Nuclide: a nuclear isotope, where X is the chemical symbol of the element, A is the mass number of the isotope, and Z is the atomic number of the element
Describe the interactions in a nucleus
Strong nuclear force: Since all protons are positive, like charges repel therefore the strong nuclear force keeps the nucleus together. It is strong, short-ranged and involves neutrons. Large nuclei need more neutrons to keep the nucleus together.
7.2: Radioactive Decay:
Radioactive decay: process in which unstable atomic nucleus’s loses energy by emitting radiation in form of particles or EM waves, resulting in the transformation of parent nuclide into daughter nuclide. Measured in Becquerel’s (Bq) transformations per second.
Alpha decay: atomic nucleus emits alpha particle, equivalent to a Helium nucleus.
Atomic masses and numbers balance on both sides of the equation
Beta decay: atomic nucleus emits beta particle (electron or positron).
In β-decay, the weak interaction converts a neutron into a proton while emitting an electron and an anti-neutrino
In β+ decay, energy is used to convert a proton into a neutron, a positron and a neutrino
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Requires energy thus cannot occur in isolation.
Gamma radiation: electromagnetic waves (high-energy photons) are emitted during radioactive decay. Nucleus is said to have changed from an excited state to a lower energy state.
Property Alpha (α) Beta (β) Gamma (γ)Effect on Photographic Film Yes Yes Yes# of ion pairs produced in air 104 per mm 102 per mm 1 per mmMaterial needed to absorb it Piece of Paper Few mm
aluminum10cm lead
Penetration Ability Low Medium HighPath Length in Air A few cm Less than 1m Infinite
Deflection by E+B fields Positive Charge Negative charge Not deflectedSpeed 107 ms-1 108ms-1 3x108ms-1
Biological effects of ionizing radiation:
Radiation sickness + burns (at first)
Could cause damage to molecules such as DNA which could lead to it ceasing to function.
Molecular damage could prevent cells from dividing and multiplying
Could cause malignant cells to grow which is called cancer
Why are some nuclei stable and unstable?
For elements with Z less than about 20, the protons and neutrons are in equal numbers. · Due to an increase in the electrostatic repulsion forces of protons as the number of protons increases, more neutrons must be found in nucleus to hold atom together. Each time protons and neutrons are added, they must go into higher energy state, and eventually become unstable. Unstable nuclei emit alpha particles (two protons and two neutrons) in order to reach a more stable state.
Half Life:
Radioactive decay is a random process not affected by external conditions. The rate of decay decreases exponentially with time.
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Radioactive half-life: The time taken for half the number of nuclides present in a sample to decay.
Nuclear reactions: Fission and Fusion
An example of artificial transmutation: Artificial transmutation is causing particles to decay by bombardment of particles. E.g. Uranium atoms bombarded with neutrons to start fission reaction
Unified atomic mass unit: 1/12th the mass of a Carbon-12 nucleus. Units created to compare atomic masses, since individual masses in nuclear reactions are very small. The mass of a proton or a neutron are approximately 1 u. Approximately 1.66 x10-27kg
Mass defect – The difference between the mass of a nucleus and the masses of its component nucleons.
Binding energy – The amount of energy that is released when a nucleus is assembled from its component nucleons
E=mc2
1eV=1.6x10-19J
1MeV=1.6x10-13J
1 u of mass converts into 931.5MeV
Fission: A nuclear reaction where large nuclei are induced to break up into smaller nuclei and release energy in the process.
Used in nuclear reactors and atomic bombs
One such reaction is bombarding a uranium nucleus with a neutron causing it to break up into two smaller nuclei.
10n+235
92U=14156Ba + 92
36Kr + 310n + energy.
Since the original neutron has created three more there is the chance of a chain reaction occurring.
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Fusion: A nuclear reaction where small nuclei are induced to join together into larger nuclei and release energy in the process.
The reaction that fuels all stars including the Sun.
Whenever a nuclear reaction (fission or fusion) releases energy, the products of the reaction are in a lower energy state than the reactants. Mass loss is the source of this energy,
A reaction is energetically feasible if the products of the reaction have greater binding energy per nucleon when compared with the reactants.
Topic 8: Energy, power and climate change:
Thermal energy may be completely converted to work in a single process, but that continuous conversion of this energy into work requires a cyclical process and the transfer of some energy from the system.
Degraded energy is energy that is the energy that is transferred from the system to the surroundings that is no longer able to produce useful work.
Sankey Diagram: The wider the arrow the more energy
Flow Diagrams
Electrical energy may be produced by rotating coils in a magnetic field
Non-renewable sources of energy are finite sources which are being depleted and will run out. They include fossil fuels (oil, natural gas and coal) and nuclear fuels such as uranium. The energy in these sources is a form of potential energy which can be released by humans. Sources that can be used up and eventually run out.
Renewable sources include solar energy (and other forms indirectly dependent on solar energy such as wind energy and wave energy) and tidal energy. They are sources that cannot be used up. Most renewable sources are related to the sun.
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The energy density of a fuel is the energy that can be obtained from a unit mass of the fuel. Energy density is measured in J/kg
The greater the energy density the better as it costs more money to move greater the amount of fuel.
Energy Density = energy release from fuel/mass of fuel consumed
State the relative proportions of world use of the different energy sources that are available.
Industrialization led to a higher rate of energy usage, leading to industries being developed near to large deposits of fossil fuels.
3 Main fossil fuels are coal, oil and natural gas
They are produced by the decomposition of buried animal and plant matter under the pressure of material on top and bacteria.
Solar Energy – Photosynthesis – Chemical Energy In Plants – Compression – Chemical Energy in Fossil Fuels – Burning – Thermal Energy etc.
Advantages
High Energy Density
Easy to Transport
Relatively Cheap
Disadvantages
Will run out
Pollution
Contributes to greenhouse effect
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Non-fossil fuel power-production:
How does a chain reaction happen:
Energy is required to split a U-236 nucleus. This can be supplied by adding a neutron to the U-236 nuclei, which increases the binding energy and causes the nucleus to split in two.
Extra neutrons are produced, which can go on to react with other U-236 nuclei in a self-sustaining chain reaction. However they must be first slowed down to less than 1 eV.
Critical mass is the minimum mass required for a chain reaction to occur.
Controlled nuclear fission : -used in power plants -prevents uncontrolled chain reactions - only used as needed
Uncontrolled nuclear fission : -used in nuclear weapons -causes chaotic explosions for maximum energy release
Fuel enrichment is the process where the fissionable material is increased to make nuclear fission more likely
Energy transformations in a nuclear power plant:
Energy released in this reaction is in the form of kinetic energy, which is converted into thermal energy before a coolant passing through the moderator extracts the energy to turn water into steam which turns a turbine and produces electricity.
Moderator – Slows down neutrons with atoms, it surround the fuel rods which are the tubes containing Uranium-235.
Heat exchanger – allows nuclear reaction to occur in a place that is sealed off from the rest of the environment
Control rods – A material that can absorb excess neutrons whenever this is necessary.
How does neutron capture of uranium-238 lead to plutonium-239:
1. Neutron collides with U-238 atom.
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2. U-238 atom fuses with neutron and creates U-239.
3. U-239 undergoes beta decay to produce Np-239.
4. Np-239 undergoes beta decay to produce Pu-239.
Importance of plutonium-239 as a nuclear fuel:
Pu-239 increases the efficiency of power station as it utilizes less-fissionable U-238
Safety issues and risks involving nuclear power:
Problems associated with mining – uranium produces radon gas which when inhaled is a major hazard
Possibility of producing materials for nuclear weapons
Radioactive waste is hard to dispose of
Potential meltdown
Problems with producing nuclear power using fusion:
Plasma needed for nuclear fusion requires high temperatures and pressure (100000°C) -Nuclear fusion is not a chain reaction (conditions must be sustained) -Unfeasible with current technology
Solar Power:
Distinguish between a photovoltaic cell and a solar heating panel in terms of energy transfers and uses
Solar panels are used for central heating or for making hot water for household use, placed on roofs of houses, consisting of metal absorber, water pipes, and glass. Energy is merely converted from solar power, electromagnetic waves of light, to heat.
A photovoltaic cell converts solar radiation into electrical energy.
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Outline reasons for seasonal and regional variations in the solar power incident per unit area of the Earth’s surface
The power per unit area received at a distance r from the sun is called the intensity I and so I=P/4πr^2
This amounts to about 1400 W/m2 and is known as the solar constant. It is the power received by one square meter placed normally to the path of the incoming rays a distance of 1.5x 1011m from the sun.
-Varying solar constant -Earth’s elliptical orbit -Tilt of Earth’s axis -Weather -Altitude of the Sun in the sky -Season –Albedo
Hydroelectric Power:
Distinguish between different hydroelectric schemes:
1. Water storage in lakes
Used by hydro-electric dams
Water falling through dam spins turbine
Turbine powers generator
2. Tidal water storage
Used in coastal estuaries
Moon’s gravitational pull causes high tides and low tides
Dam lets high tide in and forces low tide to exit by pushing a turbine
Turbine powers generator
3. Pumped storage system
Used during low-demand hours
Excess electricity is used to pump water to a reservoir
Water is released during high-demand hours (spins a turbine)
Turbine powers generator
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Energy Transformation in hydroelectric schemes:
Gravitational PE of water
KE of water
KE of turbines
Electrical energy
P=pQgh
Wind Power:
Basic features of a wind generator:
Consists of a horizontal axis with two blades
P = ½ pAv3
-Merely theoretical -Real life restrictions (wind density variation, weather conditions, wind not perfectly incident on blades)
Which shows that the power carried by the wind is proportional to the cube of the wind speed and proportional to the area spanned by the blades.
Solar energy from the sun – KE of wind – KR of turbine – Electric energy
Advantages of wind power
The source is the wind and its free
It is inexhaustible
Clean, without carbon emissions
Ideal for remote island locations
Disadvantages of wind power
Works only if there is wind
Low power output
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Aesthetically unpleasant
Best locations far from large cities
Maintenance costs high
Wave Power:
Oscillating water column – Water capture chamber set into rock face. Total power forces water into chamber. Air alternatively compressed and decompressed by OWC. Rushes of air drive the Well’s turbine, generating electrical power
The great advantage of the OWC is that the speed of the air through the column can be increased by adjusting the diameter of the valves through which the air passes. In this way high-air speeds can be attained.
A water save of amplitude A carries an amount of power per unit length of its wavefront equal to pgA2v/2 where p is the density and v is the speed of energy transfer.
Greenhouse Effect:
Solar Radiation:
The sun may be considered to radiate as a perfect emitter and emits a total power of 3.9x1026W.
P = IA. Solar constant = I = P/A = 3.9x1026 / 4(pi)(1.5x1011)2 = 1400 W/m2
Albedo
The albedo of a body is the ratio of the power of radiation reflected or scattered from the body to the total power incident on a body.
Albedo = total scattered/reflected power/ total incident power
The albedo is a dimensionless number. Snow has a high albedo which means that snow reflects most of the radiation incident on it.
The average global albedo is about 0.3. The variations depend on the season, latitude or whether one is over desert land.
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The greenhouse effect is the warming of the Earth caused by infrared radiation, emitted by the Earth’s surface, which is absorbed by various gases in the Earth’s atmosphere and is then partly re-radiated towards the surface.
Greenhouse Gas Natural Sources Anthropogenic/Human SourcesWater Vapor Evaporation of water from
oceans, rivers and lakes
Carbon Dioxide Forest fires, volcanoes, evaporation of water from oceans
Burning fossil fuels in power plants and cars, burning forests
Methane Wetlands, oceans, lakes and rivers
Flooded rice fields, farm animals, termites, processing of coal, natural gas and oil, and burning biomass
Nitrous Oxide Forests, oceans, soil and grasslands
Burning fossil fuels, manufacture of cement, fertilizers, deforestation (reduction of nitrogen fixation in plants)
Explain the molecular mechanisms by which greenhouse gases absorb infrared radiation:
Greenhouse gases absorb electromagnetic waves as a result of resonance. The natural frequency of oscillation of the molecules of the greenhouse gases is within that of infrared region.
The power radiated by a body is governed by the Stefan-Boltzmann Law.
The amount of energy radiated per second (i.e. the power) = e (5.67x10-8 W/m2/K4)AT4
The constant e is called the emissivity of the surface which is a dimensionless number ranging from 0 to 1. When e=1 we have a black body which is a theoretical body that is a perfect emitter. If a surface is black and dull such as charcoal it will have an emissivity closer to 1.
Good emitters or heat are also good absorbers of heat which is why in winter people wear dark clothes to absorb the radiation from the sun. Light-coloured surfaces are good reflectors of radiation which is why you wear light colours during the summer.
Most of the energy radiated by a body is done so at a specific wavelength that is determined by the temperature of a body. The higher the temperature, the shorter the wavelength. For a body at ordinary room temperature 193K, the wavelength at which most of the energy is radiated is an infrared wavelength.
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Graph:
The lower the emissivity the lower the curve.
We see that with increasing temperature, the peak of the curve occurs at lower wavelengths and the height of the peak increases. The relation between temperature and the peak wavelength, the wavelength at which most of the energy is emitted is given by Wien’s law.
Wien’s law = (wavelength) T = 2.90x10-3mK
The Earth’s surface emits infrared radiation because the earth’s surface is at a temperature of 288K
(wavelength) = 2.90x10-3 / 288 = 1.0 x 10-5 m
Surface heat capacity
Cs, the surface heat capacity of the body is the energy required to increase the temperature of 1m2 of the surface by 1K.
The amount of thermal energy needed to increase its temperature by T is given by Q=ACs∆T
Cs = phc
I = Cs (∆T/T)
Students should appreciate that the change of a planet’s temperature over a period of time is given by: (incoming radiation intensity – outgoing radiation intensity) × time / surface heat capacity.
Possible models of global warming:
Changes in the composition of greenhouse gases in the atmosphere
Increased solar flare activity
Cyclical changes in the Earth’s orbit
Volcanic activity
Continental drift affecting the ocean currents and winds
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Enhanced greenhouse effect refers to additional warming due to increased quantity’s of greenhouse gases in the atmosphere. The increases in the gas concentrations are due to human activity.
Analyzing very old ice core samples collected in Antarctica and Greenland among many things shows gas concentrations and atmospheric temperature at the time of freezing. This shows there is a very close link between global warming and increased greenhouse gas concentrations.
The Antarctic ice cores in particular have been analyzed to reveal a connection between temperature changes and changes in carbon dioxide and methane concentrations. The ice cores give a detailed account of global climatic conditions over a time period spanning some 420,000 years.
Mechanisms that may increase the rate of global warming
global warming reduces ice/snow cover, which in turn changes the albedo, to increase rate of heat absorption
temperature increase reduces the solubility of CO2 in the sea and increases atmospheric concentrations
deforestation reduces carbon fixation
The melting of ice
Sea ice, when melted, will not result in a change of sea level, by contrast, land ice when melted, will result in an increased sea level.
Estimating changes in sea level
Warming in general will result in a rise of sea level, not only because more land ice will melt but also because warmer water occupies a larger volume.
Coefficient of volume expansion: ∆V=(coefficient of volume expansion y) V0∆(theta)
The coefficient of volume expansion is the fractional change in volume per unit temperature change.
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Example question: The area of the oceans of the Earth is 3.6x108km2 and the average depth of water is about 3.7 km. Using a coefficient of 2x10-4 K-1 estimate the expected rise in sea level after an increase of 2K.
The total volume of water isV0 = A x d where A is the area and d is the average depth.
So A x d = 1.33x109km3 = 1.33x1018m3
Putting the numbers into the formula we get 5.3x1014m3
H=∆V/A = 5.3x1014/3.6x1014
= 1.5m
This assumes a constant coefficient, uniform heating of the water and does not take into account the initial water temperature. It also does not take into account the fact that more evaporation would talk place, hence cooling the water.
One effect on climate of a rising sea level is the change in the albedo of the surface (more water as opposed to dry land)
The expected change in temperature due to a change in albedo, because of more water covering land are small. A more significant effect of ice melting and the sea level rising is expected to be the fact that, with more water, and at a higher temperature, the evaporation rate will increase and therefore more water vapour will be released into the atmosphere. This means:
Cooling of the Earth’s surface (because latent heat is given to the water in order to evaporate)
More cloud cover (and therefore more reflected radiation)
More precipitation (i.e. rain, but not necessarily in the region of interest.
An additional effect of higher temperatures on climate is the fact that carbon dioxide solubility in oceans decreases which means more is left in the atmosphere.
Example question: Large areas of rainforests are being destroyed by cutting down (and burning. Discuss the possible effects of this on the energy balance of the region.
Answer:
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Changing forests to dry land has 3 immediate consequences. The first is that a low albedo of the dark, moist forests is replaced by a higher albedo which reduces temperatures since more radiation is reflected rather than absorbed. The second is that the evaporation rate was decreased – this tends to increase temperatures since the surface no longer has to supply the latent heat for evaporation. The third factor is that by removing and burning the trees we remove a carbon dioxide sink and produce more carbon dioxide.
Measure to reduce global warming
Using fuel-efficient cars and developing hybrid cars further
Increasing the efficiency of coal-burning [plants
Replacing coal-burning power plants with natural gas-fired plants
Considering methods of capturing and storing the carbon dioxide known as carbon capture and storage (CCS)
Increasing the amount of power produced by wind and solar generators
Considering nuclear power
Stopping deforestation
Being energy conscious with things such as buildings
The Kyoto protocol and the IPCC
The industrial nations agreed to reduce their emissions of greenhouse gases by 5.2% from 2008-2012. APPCDC asked for voluntary reductions of these emissions, it has been called worthless as the reductions are voluntary
Topic 9: Motion in Fields:
The path in projectile motion is always a parabola (e.g. catching a ball). The only forces acting in projectile motion are gravity and friction. It is moving horizontally and vertically at the same time but the horizontal and vertical components of the motion are independent of eachother.
Horizontal component: No forces in the horizontal direction, i.e. no acceleration i.e. constant velocity.
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Vertical component: There is a constant vertical force acting down (gravity)
The effect of air resistance on the trajectory of a projectile:
The path is no longer parabolic
The maximum height and range decreases
The angle at which the projectile impacts the ground steepens
Gravitational potential: the work done per unit mass in bringing a small point mass from infinity to a point. V=W/m (work done/test mass) = -Gm/r
Gravitational potential energy: The total work done in moving the mass from infinity to a point. Gpe=-Gmm/r
Equipotential surfaces and gravitational field lines are at right angles to each other
Escape speed is the speed needed to be able to escape the gravitational attraction of the planet
0.5mv2=Gmm/R
Vescape=√2GM/R
Electric potential: Work done in moving the charge from infinity to that point. V=W/q
V=(k) x (Q/r)
Electric potential energy: The work done moving a positive unit charge from the point of lower potential to the point of higher potential
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Potential due to more than one charge = Addition of all individual potentials due to the individual charges.
P83!
9.4: Orbital Motion:
Gravitation provides the centripetal force for circular orbital motion.
Derive Keplar’s 3rd law
GMm/r2=mv2/r
Gm/r2=v2/r (where v =2(pi)r/T)
R3/T2
Derive expressions for the kinetic energy, potential energy and total energy of an orbiting satellite
PE = -GMm/r
KE = .5GMm/r
Total energy = KE+PE = -.5Gm/r
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Weightlessness:
If a lift breaks and the lift and passenger accelerate down at 10ms-2 the person would spear to be weightless for the duration of the fall
An astronaut in an orbiting space station would also appear weightless
Topic 10: Thermal Physics:
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The three ideal gas laws can be combined to form pV/T = constant
The constant will depend on the number of molecules in the gas
PV=nRT
Where R = molar gas constant = 8.314 J mol-1 K-1
Difference between ideal gases and real gases:
Ideal gases follow the gas laws for all values of p, V and T and thus cannot be liquefied
Collisions are not perfectly elastic
There are intermolecular forces present
Real gases can approximate to ideal gases provided the intermolecular forces are small enough to be ignored, the pressure is low, and the temperature is high.
Absolute zero and the Kelvin scale:
Absolute zero is 0 on the Kelvin scale and -273 on the Celsius scale. It is characterized by the complete absence of heat – the point at which all atomic and molecular energy ceases. There is no kinetic energy between the molecules
Work done during expansion at constant pressure: Work = pressure (change in volume)
First law of thermodynamics: The thermal energy transferred to a system from its surroundings is equal to the work done by the system plus the change in internal energy of the system. OR Q=∆U + W
The first law of thermodynamics is a statement of the Law of Conservation of Energy in which the equivalence of work and thermal energy transfer is taken into account
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Work done in a thermodynamic cycle is the area of the quadrilateral
Second Law of Thermodynamics and Entropy
The Second Law of Thermodynamics implies that thermal energy cannot spontaneously transfer from a region of low temperature to a region of high temperature
Entropy is a system property that expresses the degree of disorder in the system
The entropy of the universe can never decrease.
Whenever thermal energy flows from a hot object to a colder object, overall the total entropy has increased
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Topic 11: Wave Phenomena:
Nature of standing (stationary)waves
Standing wave Normal (travelling) waveAmplitude All points on the wave have
different amplitudes. The maximum amplitude is 2A at the antinodes. It is zero at the nodes.
All points on the wave have the same amplitude
Frequency All points oscillate with the same frequency
All points oscillate with the same frequency
Wavelength Twice the distance from one node to the next node
Shortest distance between two points that are in phase with one another
Phase All points between one node and the next node are moving in phase
All points along a wavelength have different phases
Energy Energy is not transmitted by the wave but it does have energy associated with it
Energy is transmitted by the wav
A standing wave is the product of the propagation of 1 wave against a wall and its reflected wave with the same speed, same wavelength, same amplitude, opposite direction. Because the wave is reflected, the energy that is propagated returns to the same point of origin. Velocity=displacement / time, and since there is no displacement, the wave has no velocity. As well, we say that no energy is propagated
Nodes are points that are always at rest
Antinodes are the places where maximum movement takes place
Formation of standing waves:
When two waves of the same speed and wavelength and equal or almost equal amplitudes travelling in opposite directions meet, a standing wave is formed. It is the result of the superposition of the two waves travelling in opposite directions.
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A standing wave has nodes, points at which the displacement is always zero, and antinodes, points at which displacement is at maximum
The fundamental frequency is the first harmonic.
P93
V=fλ
11.2: Doppler Effect:
The Doppler effect us the change of frequency of a wave as a result of the movement of the source or the movement of the observer.
When a source of sound is moving towards an observer, the pitch is higher than when the source is at rest. When a source of sound is moving away from an observer the pitch is lower than when the source is at rest.
Source moving towards an observer: F’=f/ (1-vs/v)
Source moving away from an observer: F’=f/ (1+vs/v)
Where v= the speed of sound = 343 m/s
f= the frequency at rest,
vs= velocity of the source
Observer moving towards stationary source: F’= (1+ vs/v) f
Observer moving away from a stationary source: F’= (1- vs/v) f
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Doppler Effect for light: λ’= λ√ (1+v/c) / (1-v/c)
11.3 Diffraction:
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11.4: Resolution:
11.5: Polarization:
Topic 12: Electromagnetic Induction:
Describe the inducing of an e.m.f by relative motion between a conductor and a magnetic field
When a conductor moves through a magnetic field, an electromotive force is induced. It depends on the speed of the wire, strength of the magnetic field and the length of wire in the magnetic field.
Derive the formula for an e.m.f induced in a straight conductor moving in a magnetic field.
Fe=Eq = (V/I)q
Fm= Bqv
V=BIv
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Magnetic flux is defined as Φ = BA (field strength x area). If the field is not perpendicular to the area in question, however, Φ = BAcosØ, where Ø is the acute angle between the field direction and the normal to the area.
Flux linkage is basically the change in NØ, where N is the number of turns of wire, and Ø is the flux.
Faraday’s Law: The magnitude of an induced e.m.f i proportional to the rate of change of flux linkage
Lenz’s Law: The direction of the induced e.m.f is such that is an induced current were able to flow it would oppose the change which caused it
12.2 Alternating Current:
Describe the emf induced in a coil rotating within a uniform magnetic field
The induced emf is sinusoidal if the rotation is at constant speed.
Increasing the speed of rotation will reduce the time period of the oscillation and increase the amplitude of induced e.m.f.
Explain the operation of a basic alternating current (ac) generator
The coil if wire rotates in the magnetic field due to an external force. As it rotates the flux linkage of the coil changes with time and induced an e.m.f.
Discuss what is meant by the root mean squared (rms) value of an alternating current or voltage
The rms value of an alternating current (or voltage) is that value of the direct current (or voltage) that dissipates power in a resistor at the same rate. The rms value is also known as the rating.
State the relation between peak and rms values for sinusoidal voltage and currents
.
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Describe the operation of an ideal transformer
A useful device that makes use of electromagnetic induction is the ac transformer as it can be used for increasing or decreasing ac voltages and currents.
Outline the reasons for power losses in transmission line and real transformers
Resistance of the windings of a transformers result in it warming up
Hysteresis losses cause the iron core to warm up as a reult of the continued cycl of changes to its magnetism
Flux losses
Explain the use of high-voltage step-up and step-down transformers in the transmission of electrical power.
A step-up transformer increases the voltage for economic reasons; there is no ideal value of voltage for electrical transmission.
Suggest how extra-low-frequency electromagnetic fields such as those created by electrical appliances and power lines induce currents within a body
A human body is a conducting medium, so when it is moving in an alternating magnetic field at extra-low-frequency, then electric field is induced, hence inducing current in human body.
Discuss some of the possible risks involved in living and working near high-voltage power lines.
Current experimental evidence suggests that low-frequency fields don’t harm genetic material. There has been evidence that this may lead to infant cancer and infant leukaemia. These risks are likely to be dependent on current (density) frequency, and length of exposure.
Topic 13: Quantum Physics and Nuclear Physics:
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The photoelectric effect is the phenomenon where electrons are emitted from the surface of a metal after being exposed to light (of a particular frequency called the threshold frequency).
Light below the threshold frequency will not cause electrons to be emitted.
Above the threshold frequency, the maximum KE of the electrons depends on the frequency of the incident light.
The number of electrons emitted depends on the intensity of light, and not the frequency.
Emission of electrons is instantaneous, and considers that light can act as particles called photons.
Light travels in discrete, packets of energy called photons.
The energy of the photon is given by the equation E=hf, where h is Planck’s constant and f is the frequency of the light.
The photon explains the photoelectric effect because it shows that light can act as particle and not just a continuous wave of energy.
If light traveled solely as a wave, any frequency of light would cause an emission of electrons. This is not the case.
The threshold frequency exists, below which no electrons are emitted. Ephoton = Eelectron + Ekinetic hf =φ+Ekhf = hf0 + Ek Ek(max) =hf −φ
Describe and explain an experiment to test the Einstein model
Millikan’s experiment involving the application of a stopping potential would be suitable. A simple circuit was used to determine the maximum KE of the emitted electrons for various frequencies of light. The evacuated chamber consisted of two electrodes. One electrodewas exposed to incident light. If the light was above the threshold frequency for the metal electrode, a current registered in the ammeter. The voltage was reversed sothat the electrons causing the current would be repelled. The voltage that reducedthe current to zero, also called the stopping voltage can be used to calculate themaximum KE of the emitted electrons, Regardless of the intensity of thelight incident on the metal
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(which increases the current), the stopping voltage isalways the same for a given frequency.
Describe the de Broglie hypothesis and the concept of matter waves
The de Broglie hypothesis states that all particles can act and travel as waves and have an associated wavelength defined λ=p/h, where p is the momentum of the particle, and h is Planck’s constant.
Matter waves are the waves associated with particles or matter. They have an associated de Broglie wavelength.
Outline an experiment to verify the de Broglie hypothesis
The Davisson and Germer electron diffraction experiment. Davisson and Germer used an electron diffraction pattern to determine the wavelength of an electron. The experimental wavelength corresponded to de Broglie’s calculated wavelength.
KE = eV.
KE = .5mv2=p2/2m
Outline a laboratory procedure for producing and observing atomic spectra:
Matter emits light when heated to high temperatures or exposed to high electric fields. This light can be split into its component wavelengths if put through a spectrometer.
Emission spectrum: the spectrum of light that has been emitted by a gas
Absorption spectrum: the spectrum of light transmitted through a gas
Explain how atomic spectra provide evidence for the quantization of energy in atoms.
Spectral lines show that electrons shift orbits releasing or absorbing discrete amounts of energy. Electrons occupy discrete energy levels. Movement between
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levels involves absorbing or emitting energy. When an electron moves from a higher energy level to a lower energy level, it emits energy in the form of light (photons).
Explain the origin of atomic energy levels in terms of the “electron in a box” model.
P106. Important
Outline the Schrödinger model of the hydrogen atom.
The model assumes that electrons in the atom may be described by wave functions. The electron has an undefined position, but the square of the amplitude of the wave function gives the probability of finding the electron at a particular point. Electrons orbit in a probability region or electron cloud. The solution to the equation predicts exactly the line spectra of the hydrogen atom.
Outline the Heisenberg uncertainty principle with regard to position–momentum and time–energy.
P108
Students should be aware that the conjugate quantities, position–momentum and time–energy, cannot be known precisely at the same time. They should know of the link between the uncertainty principle and the de Broglie hypothesis. For example, students should know that, if a particle has a uniquely defined de Broglie wavelength, then its momentum is known precisely but all knowledge of its position is lost.
13.2: Nuclear Physics:
Explain how the radii of nuclei may be estimated from charged particle scattering experiments.
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One experiment that can be used is the Geiger Marsden experiment. An estimate of the radii of nuclei can come about through the principle of the conservation of energy. The KE of a particle approaching a nucleus is completely transformed into electrostatic potential energy. At the distance of closest approach, the KE will be converted entirely to PE. The particle will be momentarily at rest. Use of energy conservation for determining closest-approach distances for Coulomb scattering experiments is sufficient.
Describe how the masses of nuclei may be determined using a Bainbridge mass spectrometer
Students should be able to draw a schematic diagram of the Bainbridge mass spectrometer, but the experimental details are not required. Students should appreciate that nuclear mass values provide evidence for the existence of isotopes.
Describe one piece of evidence for the existence of nuclear energy levels.
When an alpha particle or a gamma photon is emitted from the nucleus, only discrete energies are observed.
Describe β+ decay, including the existence of the neutrino.
In β+ decay, energy is used to convert a proton into a neutron, a positron and a neutrino. Beta plus decay cannot occur in isolation, because it requires energy, the mass of the neutron being greater than the mass of the proton.
Beta plus decay can only happen inside nuclei when the absolute value of the binding energy of the daughter nucleus is higher than that of the mother nucleus. The difference between these energies goes into the reaction of converting a proton into a neutron, a positron and a neutrino and into the kinetic energy of these particles.
State the radioactive decay law as an exponential function and define the decay constant.
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The decay constant is defined as the probability of decay of a nucleus per unit time. If the number of nuclei present in a sample at t = 0 is N0, the number N still present at time t later is given by N = Noe-λt where λ is the decay constant (the probability that a nucleus will decay in unit time).
Derive the relationship between decay constant and half-life.
T1/2=ln2/λ)
N=N0/2
N0/2 = N0e-λt½
1/2 = e-λt½
Ln(1/2) = -λt½
λt½=-ln(1/2) =ln2
T1/2=ln2/λ
Outline methods for measuring the half-life of an isotope.
For short half-lives, the half life can usually be measured directly. For longer half lifes, values of activity can be measured and the decay law can be used to calculate λ and thus t½. Measure the activity A and chemically find the number of atoms of the isotope. Use A = λN and then λt½ = ln2
Topic 14: Digital Technology:
Option G: Electromagnetic Waves:
Outline the nature of electromagnetic (EM) waves.
Oscillating electric charge produces varying electric and magnetic fields
Electromagnetic waves are transverse, have the same speed
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Oscillating (SHM) charge produces an electric, which produces a magnetic field that is perpendicular.
Describe the different regions of the electromagnetic spectrum.
Describe what is meant by the dispersion of electromagnetic waves
Dispersion is the separating of white light into its component colours due to refraction.
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Describe the dispersion of EM waves in terms of the dependence of refractive index on wavelength.
A prism causes the dispersion of light because the refractive indexes slightly different for each of the different colours
Refraction takes place at both surfaces of the prism
Red light is bent the least and blue light is bent the most
This is because the refractive index for red light is smaller than blue
Distinguish between transmission, absorption and scattering of radiation.
Transmission - electromagnetic radiation passing from one medium to another
Absorption - Photons are absorbed by material
Can cause temperature to increase and decrease the amount transmitted
Scattering - Deflection of electromagnetic radiation from original path due to collision with particles of medium.
Discuss examples of the transmission, absorption and scattering of electromagnetic radiation
Blue light is scattered in all directions as a result of interaction with small dist particles in the atmosphere, this is why the sky appears blue
Harmful UV radiation is absorbed by the ozone layer in the atmosphere which would otherwise be harmful to creatures living on the surface of the Earth
Explain the terms monochromatic and coherent.
Coherent Waves - have a constant phase relationship.
Laser light is coherent, a light bulb is not
Monochromatic Waves - single frequency (wavelength).
Contains only a very, very narrow band of frequencies
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Laser light is monochromatic, a light bulb is not
Outline the mechanism for the production of laser light.
Light photons are produced when an atomic electron falls from a higher energy level to a lower energy level
The production of laser light involves a process that promotes a large number of electrons to a higher energy level known as population inversion.
These electrons are stimulated to fall down and emit light of a particular frequency
Or: Lower energy level electrons are pumped up to higher energy levels and stimulated to fall to energy levels corresponding to specific frequencies, producing laser light.
Outline an application of the use of a laser
Technology (bar-code scanners, laser disks)
Reading and writing of CD’s
G2: Optical Instruments:
Define the terms principal axis, focal point, focal length and linear magnification as applied to a converging (convex) lens.
Principal axis – The line going directly through the middle of the lens
Focal point - Location on the principal axis where parallel light rays converge after passing through the lens.
Focal length - Distance between the focal point and the center of the lens.
Linear magnification – The ratio between the size (height) of the image and the size (height) of the object.
It has no units
Linear magnification = image size/object size
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Define the power of a convex lens and the dioptre
The power is the reciprocal of the focal length. P=1/f
1m-1= 1 dioptre
Construct ray diagrams to locate the image formed by a convex lens.
P159
Draw two lines, one straight across to the middle of the lens and then through the focal point on the other side.
The other line goes through the principal axis in the middle of the lens and straight through.
Distinguish between a real image and a virtual image.
Real image - formed when light rays actually converge on a location and can be projected onto a screen
Virtual image - formed by light rays that only appear to converge on a location and cannot be projected onto a screen.
The thin lens formula is 1/f = 1/u + 1/v
Apply the convention “real is positive, virtual is negative” to the thin lens formula
i.e. for a virtual image, the image distance will be negative, i.e. it is one the same side as the lens
The simple magnifying glass:
Define the terms far point and near point for the unaided eye
Far point – The distance between the eye and the furthest object that can be brought into focus.
Sachin
For normal vision this is taken to be infinity
Near point – The distance between the eye and the nearest object that can be brought into clear focus.
For normal vision this is taken to be 25cm
Define angular magnification
Angle subtended at eye normally/Angle subtended at eye using instrument
Derive an expression for the angular magnification of a simple magnifying glass for an image formed at the near point and at infinity
Image formed at the near point: M=D/f + 1
Image formed at infinity: M=D/F
The compound microscope and astronomical telescope:
Construct a ray diagram for a compound microscope with final image formed close to the near point of the eye (normal adjustment)
A compound microscope consists of the objective lens and the eyepiece lens
P162
Construct a ray diagram for an astronomical telescope with the final image at infinity (normal adjustment)
P162
State the equation relating angular magnification to the focal lengths of the lenses in an astronomical telescope in normal adjustment
M=f0/fe
Length of telescope = f0+fe
Aberrations:
Sachin
Explain the meaning of spherical aberration and of chromatic aberration as produced by a single lens
Spherical Aberration: Rays striking the outer regions of a spherical lens will be brought to a slightly different focus point from those striking the inner regions of the same lens
Chromatic Aberration: Rays of different colours will be brought to a slightly different focus point by the same lens due to the difference in refractive indices
Describe how spherical aberration in a lens may be reduced
The shape of the lens could be altered, however the lens would no longer be spherical
The effect could be reduced by decreasing the aperture. However the total amount of light would be reduced and the effects of diffraction would be made worse
Describe how chromatic aberration in a lens may be reduced
The effect can be eliminated for 2 colours and reduced for all by using two different materials to make up a compound lens. This lens is called an achromatic doublet, the two types of glass produce equal but opposite dispersion
State the conditions necessary to observe interference between two sources
they must have the same phase
the phase difference between them must remain constant
Explain, by means of the principle of superposition, the interference pattern produced by waves from two coherent point sources
When two coherent point sources interfere they produce an interference pattern
The dark lines are areas where the two waves interfere destructively, in between the dark points are areas of maximum amplitude where the waves interfere constructively
Sachin
When the two waves have both travelled an integer value of wavelengths they interfere constructively (assuming the sources are in phase)
If the two waves have both travelled an integer value plus one half of a wavelength they interfere destructively.
Outline a double-slit experiment for light and draw the intensity distribution of the observed fringe pattern
Young’s double slit experiment
Describe the effect on the double-slit intensity distribution of increasing the number of slits.
as the number of slits increases:
- the number of observed fringes decreases
- the spacing between them increases
- the individual fringes become much sharper
Derive the diffraction grating formula for normal incidence
The slits are very small so that they can be considered to act as point sources
They are also very close together such that d is small (10–6 m)
Each slit becomes a source of circular wave fronts and the waves from each slit interfere
Consider the light that leaves the slit at an angle θ, the path difference between wave 1 and wave 2 is dsinθ and if this is equal to an integral number of wavelengths then the two waves will interfere constructively in this direction, similarly wave 2 will interfere constructively with wave 3 at this angle, and wave 3 with 4 etc., across the whole grating. Hence if we look at the light through a telescope, that is bring it to a focus, then when the telescope makes an angle θ to the grating a bright fringe will be observed. The condition for observing a bright fringe is therefore:
dsinθ = nλ
Sachin
Outline the use of a diffraction grating to measure wavelengths
All elements have their own characteristic spectrum.
An element can be made to emit light either by heating it until it is incandescent or by causing an electric discharge through it when it is in a gaseous state
If laser light is shone through a grating on to a screen, you will see just how sharp and spaced out are the maxima
Measuring the line spacing and the distance of the screen from the laser, the wavelength of the laser can be measured.
OR:
If white light is incident on a diffraction gradient the angle at which constructive interference takes place depends on wavelength
Different wavelengths are observed at different angles
An accurate measurement of the angle provides an accurate measurement of the exact wavelength and colour of light considered.
Spectrometer used to achieve an accurate measurement
G5
G.6.1: Explain the production of interference fringes by a thin air wedge
When the monochromatic light strikes the glass plate some of it will be reflected down onto the wedge.
Some of the light reflected from the wedge will be transmitted through the glass plate to the travelling microscope.
A system of equally spaced parallel fringes (fringes of equal thickness) is observed.
The travelling microscope enables the fringe spacing to be measured. The fringes can also be observed by the naked eye
Explain how wedge fringes can be used to measure very small separations.
Sachin
Applications include measurement of the thickness of the tear film on the eye and oil slicks.
Describe how thin-film interference is used to test optical flats
Wedge films can be used to test optical surfaces for flatness.
If a wedge is made of two surfaces one of which is perfectly plane but the other has irregularities, the observed fringe pattern will be irregular in shape. The irregular surface can then be re-polished until the fringes are all completely parallel and of equal thickness
State the condition for light to undergo either a phase change of π, or no phase change, on reflection from an interface
When light is reflected back from an optically denser medium there is a phase change of π
When light is reflected back from a optically less dense medium there is no phase change
