PHYSICS REVISION GUIDE

Ch1: Physical Measurement

SI units: metre, kg, second, ampere, Kelvin, mole, candela.

Derived: volume, density.

1.2 Measurement

Uncertainty = 0.5x the smallest value.

Random error: lots of slightly different readings.

Experimental error: problem with measuring device/method.

Percentage uncertainty = uncertainty/value

Adding values = add uncertainties.

Ch2: Mechanics

2.1 Kinematics

Velocity = displacement per unit time.

Speed = distance travelled per unit time.

Relative velocity = subtract the vectors.

Acceleration = ∆velocity/time

Average velocity = displacement/time

SUVATS:

a = (v - u)/t

s = (u + v)t/2

s = ut + 0.5at2

v2 = u2 + 2as

Positive displacement/velocity = body moving right.

2.2 Free-Fall Motion

On Earth, bodies fall with an acceleration of 9.81ms-2.

When falling, air resistance will push you up more and more until you cannot go faster.

Area beneath a velocity-time graph = displacement.

2.4 Projectile Motion

SUVAT for horizontal motion: R = v cos Θ t

SUVAT for vertical motion: h = v2sin2Θ/2g and t = 2vsinΘ/g

2.5 Forces and Dynamics

Gravitational force: W = mg. (W = weight).

Free body diagrams show the forces acting on objects.

2.6 Newton’s First Law of Motion

First law: “A body will remain at rest of moving with constant velocity unless acted upon by an unbalanced force.”

Examples: mass on a string (T = mg), parachutists (force up = force down), car (force left = force right).

Translational equilibrium: all forces are balanced.

2.7 Force and Acceleration

Momentum, ρ = mv.

Impulse: movement due to the effect of something.

Impulse is the change in momentum.

Newton’s second law of motion: “the rate of change of momentum of a body is directly proportional to the unbalanced force acting on that body, and takes place in the same direction.”

So, F = ma.

2.8 Newton’s Third Law

Newton’s third law of motion: “if body A exerts a force on body B then body B will exert an equal and opposite force.”

Example: a box on the floor, water hitting a wall.

Law of conservation of momentum: “in a system of isolated bodies, the total momentum is always the same.”

Area under a force-time graph = impulse.

2.9 Work, Energy, Power

Work done = force x distance moved in direction of force.

In general: Work = FcosΘ x ∆s (Θ is the angle between s and F).

Work done by a varying force: use average force, or find the area under a force-distance graph.

F/∆s = K (spring constant).

Gravitational potential energy (PE): the energy a body has due to its position above the Earth. PE = mgh.

Law of conservation of energy: “energy can be neither created or destroyed - only changed from one form to the other.”

Elastic collision: when both momentum and KE are conversed.

Inelastic collision - momentum/KE not conserved. For example when two bodies stick together (energy is taken to squash them together so KE is lost).

Sharing of energy: when a body explodes, the smaller part gets the most energy.

Power: work done per unit time (J/s or W).

Efficiency: (power in/power out) x 100 (for a percentage).

2.10 Uniform Circular Motion

Time period (T) - time for one cycle.

Angular displacement (Θ) - the angle swept by a line.

Angular velocity (ω) - 2π/T

Frequency (f) - 1/T.

All bodies moving in a circle accelerate towards the centre.

Centripetal force, F = mv2/r = mω2r (e.g. ball on a string, car on a bend, wall of death).

Ch3: Thermal Physics

3.1

The mole: 6.022 x 1023 atoms/molecules of an element.

Internal energy: the material of the object takes energy, molecules vibrate more. The total internal energy of a substance is the total PE and random KE of the molecules.

Heat flows from hot to cold between two touching bodies until a thermal equilibrium is reached.

C to K: add 273.

3.2 Thermal Properties of Matter

Thermal capacity (c): the amount of heat needed to raise the temperature of a substance by 1C. Unit: JC-1. Given by: C = Q/∆T

Specific heat capacity (C): the amount of heat required to raise the temperature of 1kg of a substance by 1C. Unit: JC-1.

When matters change state, the energy used enables the molecules to move more freely (KE is the same), so temperature does not change.

Boiling takes place throughout the liquid, at the same temperature.

Evaporation takes place at the surface only, at all temperatures. Faster molecules escape, average KE decreases, temperature decreases.

Specific latent heat (L): the amount of heat needed to change the state of 1kg of the material without a change in temperature. Unit: JKg-1. L = Q/m.

Solid to liquid: latent heat of fusion.

Liquid to gas: latent heat of vaporisation.

3.3 Kinetic Model of an Ideal Gas

- Molecules are perfectly elastic

-Molecules are perfect, tiny spheres

-Molecules are identical

-There are no forces between the molecules, except when they collide, so they move with constant velocity

-The molecules are very small; their total value is much smaller than the volume of the gas

The temperature is a measure of the average KE of the molecules of an ideal gas.

Increase in temperature and decrease in volume always increases pressure. Pressure = force/area.

Doing work on a gas = increase in KE = increase in temperature and pressure.

3.4 Thermodynamics

Absolute zero: the temperature of the gas when the pressure is zero. The point at which the molecules stop moving. -273C, 0K.

A fixed point used to define the temperature scale is something observable. The one used to define the absolute temperature scale is the ‘triple point’ water - the temperature at which it exists as a solid, liquid and gas at equilibrium (0.01C).

Equation of state for an ideal gas: PV = nRT. (R = 8.31).

Isobaric: constant pressure.

Isochoric: constant volume.

Isothermal: constant temperature.

Adiabatic: no heat exchanged (Q = 0).

A real gas: forces between molecules as the pressure/volume decreases. This makes them change to a liquid, unless the temperature is very high.

3.5 Thermodynamic Processes

A thermodynamic system is a collection of bodies that can do work on each other and transfer heat. In IB we only use the gas piston example.

Work done = P x ∆V.

Gas does work = pushes piston out = positive.

Work done on gas = piston drops down = negative.

Area under a pressure-volume graph = the work done.

First law of thermodynamics: “if a gas expands and gets hot, heat must have been added.” This is a statement of the principle of energy conservation.

Q = ∆U + W. (∆U is internal energy, Q is amount of heat added).

Isobaric: temperature, internal energy and work done decrease. Q is negative.

Isochoric: volume stays the same, temperature and internal energy increase. Q is positive.

Adiabatic contraction: volume is reduced, work done is negative, temperature/internal energy increase.

A-B: isochoric temperature rise (gas gets hot, heat added).

B-C: isobaric expansion (heat added = increase in internal energy and volume).

C-D: isochoric temperature drop (gas gets cold and loses work to surroundings).

D-A: isobaric compression (heat lost = work done on the gas, volume decrease).

A-B: isothermal (work done by gas = heat gained).

B-C: adiabatic (gas does work and cools down).

C-D: isothermal (work done so it cools down).

D-A: adiabatic (work done on gas, gas gets hotter).

3.6 Second Law of Thermodynamics

Second law: “it is not possible to convert heat completely into work”.

This implies that thermal energy cannot spontaneously transfer from a region of low temperature to a region of high temperature. Heat flows from hot to cold. Particles fly in random directions. Molecules start ordered, but start to collide and become disordered.

Rewritten: “in any thermodynamic process, the total entropy always increases” (e.g. a fridge: food gets colder, more ordered. Room is given heat, less ordered).

Entropy of a system = the amount of disorder in the system/the spreading out of energy.

Change in entropy, ∆S = Q/T (JK-1)

Ch4: Simple Harmonic Motion and Waves

Cycle: 1 complete oscillation (2π for a circle).

Equilibrium position: the place it would rest if undisturbed/displacement = 0.

Amplitude (x0): maximum displacement.

Time period (T): time taken for 1 cycle.

Frequency (f): number of complete cycles in one second.

Angular frequency (ω): ω = 2πf. (2πrads s-1 is one revolution per second).

SHM: acceleration is proportional to the distance from a fixed point. Acceleration is always directed towards a fixed point. a = -ω2x.

Displacement-time graph: x = x0 cos ωt

Velocity-time graph: v = -v0 sin ωt

Acceleration-time graph: a = -a0 cos ωt

Speed = circumference/time period = 2πr/T, but 2πr/T = ω, so speed = ω.

Centripetal acceleration= v2/r = ω2r2/r = ω2r

Acceleration = -ω2x

Maximum velocity = ωx0

V = ω√ x0−x2

4.2 Energy Changes During SHM

KE is max when displacement is zero (it is stationary at x0). KEmax = 0.5mω2x02 or 0.5mω2(x0

2 - x). PE = 0.

PE is max when the bob is at the highest displacement. PE = 0.5mv02cos2ωt = 0.5mω2x2.

If KE and PE graphs are added together, it gives a constant value known as the ‘total energy’. ET = mω2x0

2.

4.3 Forced Oscillations and Resonance

In oscillating systems there is always friction and sometimes air resistance. The system has to do work against these, resulting in a loss of energy. This is called ‘damping’ (for example, dampers in a car’s suspension to absorb the shock of a bump).

Light damping: small opposing forces, gradual energy loss, amplitude decreases over time.

Critical damping: resistive force is so large it returns to its equilibrium position.

Natural frequency: the frequency the oscillation is naturally at.

Forced oscillation: when the system is forced to oscillate at a different frequency.

Resonance: an increase in amplitude that causes the system to oscillate at its natural frequency.

Out of phase: two identical waves moving at different times.

Phase difference: the amount they are out of phase by. If completely, it is π.

4.4 Wave Characteristics

Wave pulse: when a disturbance can be seen travelling from one end to the other.

Continuous progressive waves move with SHM in the shape of a sine curve.

Transverse waves: disturbance is perpendicular to the direction of the waves.

Longitudinal waves: disturbance is parallel.

v = fλ (velocity = distance/time, therefore v = λ/1/f = fλ).

All electromagnetic waves travel with the same speed in free space.

4.5 Wave Properties

Wavefront: line joining points that are in a phase.

Rays: shows the direction of the waves. Always at a right angle to waves.

Circular wavefront: caused by a point disturbance.

Plane wavefront: extended disturbance.

Reflection: wave hits barrier and bounces back. The normal is drawn at 90 degrees. The angle of incidence = angle of reflection. The incident and reflected rays are in the same plane as the normal. In a change of medium, some waves pass through (transmitted) and others are reflected.

Refraction: there is a change in velocity when there is a change in medium. Wave hits boundary at an angle and there is a direction change.

Snell’s Law: sin i / sin r = v1/v2 (angles of incidence and refraction)

The ratio is called the refractive index. Larger = larger angle.

Diffraction: takes place when a wave passes through a small opening/aperture. If the path difference = d, then the phase angle, = πd/λ

Coherent waves = identical waves.

A polarized wave travels in one direction.

4.6 Standing (Stationary) Waves

Peaks move up and down but do not progress = a standing wave. Occurs when identical waves travelling in opposite directions superpose.

Node: place on the wave that doesn’t move at all.

Anti-node: max amplitude.

<---- IN AIR

First, f1 = v/2L, λ = 2L.

Second, f2 = v/L, λ = L

Third, f3 = 2/3L

Frequency spectrum: highest at 100Hz, 200, 300, 400 (decreases).

<---- IN A CLOSED PIPE

F1, λ = 4L.

F2, λ = 4/3L

F3, λ = 4/5L

Frequency spectrum: only add numbers formed.

<--- IN AN OPEN PIPE

F1, λ = 2L

F2, λ = L

F3, λ = 2/3L

4.7 The Doppler Effect

Wavelength ahead becomes squashed as source catches up with it.

Observed frequency, f1 = e/λ1 = cf0/c - v

Waves behind source, f2 = cf0/ c + v

Moving observer: velocity of sound is faster when closer.

Approaching f1 = (c + v)f0 /c

Receding f2 = (c - v)f0 /c

Doppler effect applies to electromagnetic radiation too. If relative velocities are smaller than the speed of light then ∆f = v/c x f0 (v = relative speed of source and observer, f0 = original frequency).

Red shift: light moving away has a longer wavelength, which is red.

Doppler effect is used in speed cameras. It reflects electromagnetic radiation off the car, and the frequency of the reflected beam is used to calculate the car’s speed.

4.8 Diffraction at a Single Slit

Huygen’s Construction:

Narrow slit: one wavelet goes through, circular.

Wide slit: all wavelets go through, sum of all wavelets.

Waves passing through a small slit will propagate.

Central maximum: directly ahead of the slit. If point is a long way away then the wavelengths are parallel and in phase, so it is brighter (high intensity).

First minimum: wave travel at an angle, so they don’t all travel the same distance (cancel each other out, low intensity).

Deriving first minimum angle: sin Θ =

λ2b2

= λb

Angles are small; in radians sin Θ = Θ, so Θ = λb

4.9 Resolution

The Rayleigh Criterion: 2 points will be resolved if the central maximum of the diffraction pattern formed of one point, coincides with the first maximum of the other (when they overlap they look like one).

If the distance between the central maxima is less than half the width of the maxima, the points will not be resolved. The width is defined by the position of the first minimum,

Θ = λb

, or for an aperture: 1.22λb

.

Increasing resolution - use different radiation wavelength.

CDs: pits are 5x107m wide. 780nm laser. Any smaller and the difference between pits and gaps aren’t recognised. To solve, use laser of 640nm.

Electron microscope: closest points that can be resolved are 200nm apart. Decreasing wavelengths doesn’t work, not visible enough. Use electrons (0.02nm) instead - can see up to 0.1nm.

Radiotelescopes: detects radiation from space. 20cm wavelengths (radiowaves), so telescopes must be huge (e.g. Lovell telescope has 76m diameter).

4.10 Polarization

When a transverse wave is polarized, the disturbance is in only one plane (i.e. through a slit), is polarized. Through a slit is vertical, so they cannot pass through horizontal slits.

To polarise light, pass it through a Polaroid (type of plastic).

Brewster’s Law: when the angle between the reflected ray and refracted ray is 90 degrees, polarization is 100%.

Brewster’s Angle, = tan-1n, when n = refractive index (sin i / sin r).

When light passes through a polarizer, intensity decreases by 50%. If it then passes through a second polarizer (an analyser), the intensity reduction depends on the angle between the polarization planes of the two polarizers. If parallel, all is transmitted. Perpendicular, none is transmitted. Between 0 and 90 degrees, some is transmitted.

Passing through an analyser, only the component of amplitude in the direction of the polarization plane passes through: A0 cos Θ.

Intensity (I) is proportional to A2, so if original intensity is (I0) then: I = I0 cos2 Θ (Malus’s Law).

4.11 Uses of Polarization

‘Optically active substances’ can rotate the plane of polarization (e.g. if put between 2 planes, it will allow light to pass through).

Angle of rotation is related to concentration of the sugar solution. To find concentration, rotate analyser until you find max brightness. Analyser angle gives angle of rotation allowing concentration to be calculated.

Angle of rotation is affected by stress (amount of force) a material is subjected to. Coloured patterns are revealed when viewed in a polarized light, allowing for stress analysis.

LCDs: each pixel is made of liquid crystal. They rotate the plane of polarization through 90 degrees when a battery is not connected to them. If the liquid crystal is placed between two crossed polarizers then it goes dark when a battery is connected.

A picture is made by applying a potential difference (connecting a battery) to selected pixels.

Ch5: Electrical Currents

The flow = the current. The ‘charge’ flows. Unit of charge is coulomb (C). Charge flows from + (higher PE) to - because electrons are negative.

Current is flow of charge (A) = charge/time.

Potential difference: the amount of work done per unit charge (V) in taking a small +ve charge from A to B. V = W/q.

Resistance (R) doesn’t let as much current flow. R is proportional to L/A.

Resistivity (ρ) is the constant of proportionality, so: R = ρL/A.

Ohm’s Law: V = IR.

Ohmic conductor: graph of VI is a straight line. Non-ohmic conductors: graph of VI is not straight.

On an ohmic VI graph, resistance is found by 1/gradient. V/I for non-ohmic conductors.

5.2 Electric Circuits

Emf (electromotive force) is the amount of chemical energy converted to electrical energy per unit charge (V).

P.d. across a resistance is the amount of electrical energy converted to heat per unit charge (V).

Resistance of the cell = internal resistance. Converts the electric energy to heat, less to be converted in the resistor, so p.d. of resistor is greater than the emf of the cell.

Current from battery = I = ε/ R + r

In a perfect battery, power = chemical energy converted to electrical energy per unit time = εI.

Power dissipated is the amount of electrical energy converted to heat per unit time. P = VI.

Power can also be: P = I2R and P = V2/R.

In a series circuit, R = R1 + R2 + R3...

In a parallel circuit: R = 1/R1 + 1/R2 + 1/R3...

P.d. of cells in series: V1 + V2...

Ideal voltmeter: infinitely high resistance (doesn’t take current).

Ideal ammeter: zero resistance (doesn’t change current in the circuit).

Electrical sensors: a device whose electrical properties change with changing physical conditions.

Thermistor: resistance decreases as temperature increases.

Light sensor (LDR): more light means lower resistance.

Strain gauge: thin metal wire. If stretched the cross-section is smaller, giving a higher resistance.

Potential dividers vary p.d. (have two series resistors).

Vout = Vin x R2

R1+R2

For example, an automatic light switch: no light on the LDR = more resistance = more Vout = activates electronic switch to turn lights on (needs min. P.d.).

Strain gauges can be used to measure how much a building is stretched by using Vout. For example, underneath a bridge.

Ch6: Fields and Forces

Newton’s universal law of gravitation: everything in the universe is attracted to everything else. (“Every single point pass attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of their separation”.)

Universal gravitational constant, G = 6.67x10-11

F = Gm1m2r2

(Spheres follow the same rule.)

Gravitational field strength, g, is the measure of how much force a body will experience in a field (force per unit mass experienced by a small test mass). g = F/m. For Earth it is 9.81.

g = G x M/r2 for a sphere.

For addition of fields, use Pythagoras between two points. For example:

(The red line).

6.2 Gravitational Potential

Gravitational potential: the work done per unit mass taking a small test mass from a position of zero potential to point P.

Gravitational potential energy is the PE gained by an object as its height above the ground increases (position in gravitational field). gh = PE/m.

Equipotential: travelling along a field perpendicular to the field (no work done, no change in PE). ΔV/Δh = g. Or potential gradient = field strength.

If the lines of equipotential are closer, the field is stronger.

Integrating distance from M vs Force graph gives:

W = -GMm/R, so potential (V) = W/m = -GM/r

Positive gradient and negative field strength gives: g = -Δv/Δx. Wells prove this.

Adding potentials=( -GMA/rA) + (-GMB/rB)…

Lines of equipotential for two objects:

6.3 Escape Speed

Escape speed: “the speed needed for an object to reach a distance at which it is no longer attracted back to the earth”.

PE = -GMm/r

Loss of KE = gain in PE

1/2mv2 = -GMm/R2 - -GMm/RE

Substitute R2 for infinity: 1/2mv2 = -GMm/RE

Rearrange: Vescape = √ 2GMRE (for Earth it is 11km/s-1)

6.4 Orbital Motion

Gravitation provides the centripetal force for circular orbital motion.

Equating the two equations for centripetal force:

mω2r = GMm/r2

Substituting in ω = 2π/RT:

m ¿2r = GMm/r

Rearrange: T2/r3 = 4π2/GM (M = mass of the sun).

So for planets orbiting the sun, T2/r3 is a constant, or T2 ∝ r3 (Kepler’s third law). Closer planets to the sun have a shorter time period.

Orbiting bodies: PE = -Gmm/r, KE = 1/2mv2

Equating: GMm/r2 = mv2/r

Rearrange and multiply by 0.5: KE = GMm/2r

Total energy is PE + KE = -GMm/r + Gmm/r

Total energy = -GMm/2r

Earth satellites: closer ones have a shorter time period. Lower orbits have lower energy (lower PE), but greater KE because of this. So:

Weightlessness: in deep space, gravitational fields cancel out due to distance. In free-fall with a room, the only force on you is weight. In orbital motion around earth, the pulling force on you and satellite towards Earth is equal.

6.5 Electric Force and Field

Electric force: the attraction/repulsion between objects.

Law of conservation of charge: “charge can neither be created nor destroyed”.

Coulomb’s Law states that “the force experienced by two point charges is directly proportional to the product of their charge, and inversely proportional to the square of their separation”.

F = KQ1Q2/r2 (k = 9x109).

Electric field: a region of space where a charged object experiences a force due to its charge.

Electric field strength is a measure of the force that a positive charge would experience per unit charge per mass if placed in a field. Field strength: E = F/q.

Field lines are in the direction a positive charge would move.

In a uniform field, E = F/q between two charged plates.

Close to a sphere of charge, E = K x Q/r2.

Addition of field strength: use Pythagoras.

6.6 Electric Potential

Electric potential at a point is the amount of work per unit charge needed to take a small positive test charge from a plane of zero potential to a pont.

Electric potential energy: “moving a positive electron in a field increases KE and therefore PE, giving it energy”.

Electric potential energy, VB = Eh

Electronvolt: the energy gained by an electron accelerated through a potential difference of 1V.

E = ΔV/Δh gives field strength and potential gradient.

Potential due to a point charge: W = kQq/r and potential V = kQ/r.

Potential gradient is related to field strength by: dV/dx = -E.

Equipotential for a dipole:

6.7 Magnetic Force and Field

Moving charges give rise to magnetic fields.

A magnetic field is a region of space where a small test magnet experiences a turning force.

Magnetic field lines show the direction a north pole would face.

Magnetic flux density (B): “how strong a field is. Measured in Tesla (T).

Fields caused by currents: use grip rule. Fingers curl in direction of field (ring hand), thumb shows current direction. Works only for coils/solenoids.

Force on a current-carrying conductor: force depends on field strength (flux density), uwire length, current.

F = BIL.

Left hand rule: FFC. Right hand rule: MFC.

Charges in magnetic fields: the sum of all forces on electrons = the total force on a wire. Direction on a force charge is perpendicular to the direction of motion, creates circular paths.

The force on charge q moving with velocity v perpendicular to field B is given by: F = Bqv.

6.8 Electromagnetic Induction

A conductor in a magnetic field will have different charges at the end due to the electrons moving in the direction of the force, and causing the lattice atoms to become positive. Creates a p.d. between two ends; B pushes electrons left, E pushes them right.

Current flows from high to low potential.

Connect a battery and a current will flow.

Induced emf: “ the amount of mechanical energy converted to electrical energy per unit charge”.

Max p.d. is when the magnetic force pushing electrons left equals the electric force pushing them right.

FB = FE

Velocity is v, field strength is B: FB = Bev

Electric force is due to E, and E = -dV/dx. The field is uniform so potential gradient = V/L, so:

FE = EE = Ve/L

Ve/L = Bev

Induced emf = Blv

In a non-perpendicular field, emf = BsinΘ x Lv

Faraday’s Law: “the induced emf is equal to the rate of change of flux. E = dφ/dt.

Magnetic flux: “a measure of the strength of a magnetic field over a given density”.

Flux density ∝ number of field lines. Tesla metre2.

Flux cut per unit time = emf = BLv.

Magnetic flux linkage: the total flux passing through a circuit formed by a closed conductive loop.

Lenz’s Law: the direction of the induced current is such that it will oppose the charge producing it. E = -dNφ/dt.

6.9 Alternating Current

A coil rotating in a uniform magnetic field: emf is reduced when the coil cuts the field, and the current in the coil stays the same but changes in the resistor circuit after each half revolution (due to slip ring moving).

Induced emf = flux, = BAcosΘ

With N turns: N = BANcosΘ

Substitute: N = BANcosωt

To find peak value, E0 = BANω

Increasing angular speed: shorter between peaks, higher peaks. (Faster = faster change of flux = greater emf).

Alternating current (AC) – rotating coil. Direct current (DC) - a battery.

For AC calculations we use root mean square (rms) as it is a sort-of average.

Rms – the square root of the mean of the squares.

Emf from AC varies sinusoidally (sine curve), so the rms emf and current will be the same as the root of the mean of the squares in a sine function.

IRMS = I0/√2 (I0 = peak current).

Power in AC circuits: Irms x Vrms

Transformer: primary coil is connected to an AC to make a changing magnetic field in the coil. Makes the iron core temporarily magnetic – causes changing magnetic field and emf in secondary coil.

NP/NS = VP/Vs

Power in = power out (for an ideal transformer as they have 100% efficiency), so:

VpIp = VsIs (they are rms values).

6.10 Transmission of Electrical Power

Electricity is transferred via electrical cable. Some is lost due to resistance: R = ρL/A.

To reduce power loss, we reduce the current by stepping up the voltage before transmission, or we add more cables in parallel to decrease resistance.

Power lines carry large AC currents which radiate magnetic fields. These can induce small currents in human bodies, however it is less harmful than the Earth’s magnetic field (unless sat on the power lines).

Ch7 Atomic and Nuclear Physics

Thomson model: the plum pudding model. Positive pudding with negative plums (electrons).

Rutherford model: like a mini solar system. The flaw was that the electrons would radiate electromagnetic waves, lose energy and spiral into the nucleus.

Atomic spectra: give atoms energy and they produce light as the electrons travel up the shells. Split up the light to find the different wavelengths.

Electrons only have certain amounts of energy in the first place (quantized). This is shown by the atomic spectrum as it only releases certain amounts of energy (the thin lines). This means that only certain energies are possible for different elements (proves energy levels) – discrete.

This means light must be quantized, as it is not a continuous wave.

7.2 Quantum Nature of Light

Photoelectric effect: electrons are only emitted if the light source is very bright. If it is dim, we expect no electrons to be emitted. If some are, there is a time delay as they collect energy. Lower frequency light will work if still bright enough.

Zinc plate experiment: a zinc plate on an electroscope with UV light shining on it. Lost electrons means less charge, so electroscope leaf should fall during the photoelectric effect. But: when dim, there was no time delay, but fell slower. Lower frequency (despite intensity) did not emit any electrons.

These are explainable if light is quantized.

Quantum light model: made up of packets of energy called photons. E = hf for photon.

UV has a high frequency, so it gives enough energy to the zinc plate to emit electrons. Lower intensity means less photons, means less rapid electron loss (but no delay). Low frequency means low energy photons, means it cannot free electrons.

Millikan created an experiment to find the KE of electrons. He created and electric field and increases the energy until no electrons could pass through. He used this stopping potential to find the fastest KE:

KE loss = PE gain

1/2mv2 = VSe

KEMAX = VSe

Higher intensity = higher current, same potential. (More plates but the same energy amount VS).

Threshold frequency: the frequency at which photoelectrons are liberated.

Max photoelectron KE = energy of photon – energy needed for release

KEMAX = hf – φ (φ = work function.)

OR KEMAX = hf – hf0

For photon frequency, change in energy ΔE = hf (for energy levels).

Absorption spectrum: has white lines in the rainbow where electron has absorbed the frequency needed for them to escape. Proves electron energy levels.

7.3 Wave Nature of Light

Electron gun: filament is made hot by AC current. Electrons are liberated. They accelerate towards anode by accelerating p.d. Pass through with constant velocity:

V = √ 2VemPhosphorescence: light emitted by electron when going down energy level(s).

De Broglie Hypothesis: all matter has a wave-like nature. Λ = h/ρ

For example, electrons passed through a thin film of graphite create a diffraction pattern (wave-like property).

Probability waves: diffraction maps out all the possible results.

Davidson-Germer experiment: a beam of electrons reflected off a nickel crystal. Angle of max intensity can be explained in terms of constructive interference between De Broglie waves reflected off layers of atoms (supports De Broglie hypothesis).

Heisenberg uncertainty principle: we cannot know momentum and positive accurately. We can either: pass through a small slit (know definite location, but it will be diffracted – momentum?) or pass through a large slit (definite momentum, will not deflect, so no definite location).

For momentum and displacement: Δρ Δx > h/4π

For energy and time: ΔE Δt > h/4π

7.4 Quantum Atom Models

Electron in a box: an electron isn’t free to move outside the atom. To model this, think of a string clamped at both ends. It can only have certain frequencies (the harmonics), like an electron can only have certain energies. To create a quantum model, think of it as a probability wave trapped in a box.

Schrodinger’s Model: he realised the electrons position probability was not as simple as the sine wave used previously. The wave function is called Schrödinger’s equation (ϕ) and the probability of finding the electron is ϕ2. His model predicted the most likely electron position. It showed that some energy transitions are more likely, and why some spectral lines are brighter.

For Hydrogen:

7.5 Nuclear Structure

Nuclide: proton/neutron combination that forms a nucleus.

Nucleon: a particle in the nucleus

Isotope: same proton number, different neutron number.

Ions: different number of electrons.

Nucleon number (A): protons + nucleons.

Proton Number (Z) – protons.

Mass of the nucleus: found using mass spectrometer. Projected at right angles to a uniform field; path radius ∝ mass. m = BQr/v.

The ion experiences two forces (magnetic force and electric force) so v = E/B.

Counting the number of dots on the photographic plate is the number of ions.

Charged particle scattering experiment: like Geiger-Marsden experiment. Deflected alpha particles hit a nucleus. The KE can be calculated, and distance too. To find the nucleus size, they fired faster alphas until they no longer returned. The faster ones got the closest.

Nuclear force: very short, short range force holding nucleus together (same for all nucleons).

Binding energy: the amount of work required to pull apart a nucleus. E = mc2. The energy is converted to mass (not KE, as the nucleus is not moving).

The binding energy curve of a nucleus is found by the difference between the mass of the nucleus and mass of the parts (the mass defect).

Large nuclei are less stable as they have more protons pushing the nucleus apart. All systems will try to reach the lowest possible energy. BE is released when a nucleus is formed, so changing to higher BE means energy is released (so higher BE = good/more stable).

Nuclear mass is measured in (u). 1u = 931.5MeV.

BE = mass defect.

BE per nucleon = mass defect/nucleon number.

7.6 Radioactive Decay

Alpha particles (42H): very ionizing, short (5cm) range, ~5MeV energies. Alpha decay emits 2

protons and 2 neutrons. DISCRETE.

Beta Minus Decay: not very ionizing, about 30cm range. Emits 1 neutron and gains a protons. Emits a beta-minus particle (e’) and antineutrino (v). CONTINUOUS.

Beta Plus Decay: a beta plus is a positive electron (positron). A proton changes to a neutron, a neutrino is produced. Loses a proton, gains a neutron, emits a beta plus particle and a neutrino. CONTINUOUS.

Gamma Radiation: electromagnetic radiation, no change in particles. DISCRETE.

Decay chain: when something decays into another radioactive nucleus, and then decays again.

The neutrino was made to explain beta decay, as beta cannot have a range of energies.

Health: radiation sickness can affect the nervous system and can cause hair loss, sickness, bleeding, diarrhoea and death. Long term exposure can cause cancer and genetic mutation.

7.7 Half Life

Radioactive decay is a random and spontaneous process and the rate of decay decreases exponentially with time.

Half-life: how long it takes for half of the nucleus to decay.

Rate of decay ∝ number of undecayed nuclei, so:

dN/dt = -λN (λ is the decay constant).

Integrate between time 0 (N = N0) and time t (N = NR):

Nt = N0e− λt (The exponential decay equation.)

The radioactive decay law is an exponential function. The decay constant tells us how quickly a material will decay. A large decay constant = a shorter half-life.

Λ and half-life: t1/2 is half-life, N0 is original number, so:

t1/2 = N0/2, substitute in N0/2 = N0e− λt

Cancel: ½ = e− λt

Take ln: ln(1/2) = -λt1/2

Same as: ln(2) = λt1/2

At = A0e− λt

Measuring half-life: measure activity over a period of time, or change the number of nuclei.

Potassium-Argon dating: rock is heated and releases Argon. The half-life is 1.26x109 years.

Carbon dating: use C14/C12 to get: % now = % originally x e− λt. Original % = 10-10%.

7.8 Nuclear Reactions

Transmutation: changing a nucleus by adding nucleons.

Artificial/induced transmutation: for example, nitrogen to carbon.

147N + 1

0n 146C + 1

1p (Nitrogen absorbs a neutron and emits a proton.)

Nuclear fusion: nuclear fusion is the main source of the sun’s energy. It is the joining of two small nuclei to form one big one. Greater mass = greater BE (shown by graph).

Nuclear fission: nucleus splits into two smaller nuclei. The total BE increases again.

DEFINITIONS

Newton’s first law: “A body will remain at rest of moving with constant velocity unless acted upon by an unbalanced force.”

Newton’s second law of motion: “the rate of change of momentum of a body is directly proportional to the unbalanced force acting on that body, and takes place in the same direction.” F = ma.

Newton’s third law of motion: “if body A exerts a force on body B then body B will exert an equal and opposite force.”

Gravitational potential energy (PE): the energy a body has due to its position above the Earth. PE = mgh.

Law of conservation of energy: “energy can be neither created or destroyed - only changed from one form to the other.”

Elastic collision: when both momentum and KE are conversed.

Power: work done per unit time (J/s or W).

Thermal capacity (c): the amount of heat needed to raise the temperature of a substance by 1C. Unit: JC-1. Given by: C = Q/∆T

Specific heat capacity (C): the amount of heat required to raise the temperature of 1kg of a substance by 1C. Unit: JC-1.

Specific latent heat (L): the amount of heat needed to change the state of 1kg of the material without a change in temperature. Unit: JKg-1. L = Q/m.

Absolute zero: the temperature of the gas when the pressure is zero. The point at which the molecules stop moving. -273C, 0K.

Second Law of Thermodynamics: work cannot be completely transferred into heat/in any thermodynamic process, the total entropy always increases” (e.g. a fridge: food gets colder, more ordered. Room is given heat, less ordered).

Entropy of a system = the amount of disorder in the system/the spreading out of energy.

Potential difference: the amount of work done per unit charge (V) in taking a small +ve charge from A to B. V = W/q.

Emf (electromotive force) is the amount of chemical energy converted to electrical energy per unit charge (V).

P.d. across a resistance is the amount of electrical energy converted to heat per unit charge (V).

Power dissipated is the amount of electrical energy converted to heat per unit time. P = VI.

Newton’s universal law of gravitation: everything in the universe is attracted to everything else. (“Every single point pass attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of their separation”.)

Gravitational potential: the work done per unit mass taking a small test mass from a position of zero potential to point P.

Gravitational potential energy is the PE gained by an object as its height above the ground increases (position in gravitational field). gh = PE/m.

Escape speed: “the speed needed for an object to reach a distance at which it is no longer attracted back to the earth”.

Electric field: a region of space where a charged object experiences a force due to its charge.

Electric field strength is a measure of the force that a positive charge would experience per unit charge per mass if placed in a field. Field strength: E = F/q.

Electronvolt: the energy gained by an electron accelerated through a potential difference of 1V.

A magnetic field is a region of space where a small test magnet experiences a turning force.

Induced emf: “ the amount of mechanical energy converted to electrical energy per unit charge”.

Threshold frequency: the frequency at which photoelectrons are liberated.

Nuclear force: very short, short range force holding nucleus together (same for all nucleons).

Binding energy: the amount of work required to pull apart a nucleus. E = mc2. The energy is converted to mass (not KE, as the nucleus is not moving).

Transmutation: changing a nucleus by adding nucleons.