*Modern Physics
*Max Planck proposed that an atom can absorb or emit energy only in chunks known as quanta.*The energy, E ,of each quantum depends on the frequency of the radiation E= hfh= 6.626 x 10-34 J·s (Planck’s constant)*Einstein suggested that a fundamental property of electromagnetic radiation consists of quanta of energy known as photons. E = hf = hc/λ
* In this “quantum-mechanical” picture, the energy of thelight particle (photon) must overcome the binding energy of the electron to the nucleus.* If the energy of the photon exceeds the binding energy, theelectron is emitted with a KE = Ephoton – Ebinding.
PHOTO-ELECTRIC EFFECT
“Light particle”
Before Collision After Collision
Einstein used the photon hypothesis to explain the Photoelectric effect ( emission of electrons from a metal surface when a light is incident on it)
THE ELECTROMAGNETIC SPECTRUMShortest wavelengths(Most energetic photons)
Longest wavelengths(Least energetic photons)
E = hn = hc/lh = 6.6x10-34 [J*sec](Planck’s constant)
There is a threshhold negative potential, the stopping potential, V0 , below which no current will flow into the circuit
Each light intensity has a maximum current flow, but the stopping potential remains the same
*When V is negative, only electrons with a kinetic energy greater than |eV0| can reach the anode, the maximum kinetic energy is given by eV0 .*( mv½ 2 )max = eV0 = hf –φ*φ = work function ( energy needed to release an electron from the metal)
*Special relativity
*Special relativity - the laws of physics are same in all inertial frames of reference
*Invariance of c - the speed of light in a vacuum is a universal constant ( c ) which is independent of the motion of the light source
*Lorentz contraction*An observer moving with respect to an object will observe it to be contracted along the direction of motion by the factor*A perceived reduction in the length of an object*Negligible at the speeds we experience everyday but would be noticeable at velocities comparable to that of light
For more information see http://www.fourmilab.ch/cship/lorentz.html
Time dilationThe time lapse between two events is dependent on the relative speeds of the observer’s reference frames
* Einstein’s mass-energy equivalence
*The total energy of a mass m moving at a velocity v is given by *So when v = 0 , E= mc2
*Alpha, Beta, & gamma radiationα Alpha particles are produced from the
radioactive decay of heavy elements such as uranium. They are composed of two neutrons and two protons identical to the nucleus of a helium atom. Because of their relative size and electrical charge from the two protons, alpha particles can travel only a very short distance in any material. For example a normal sheet of paper can stop alpha particles.
β Beta particles are electrons that come from transformation of a neutron in the nucleus of an atom to a proton. They can travel up to about five meters in air and one centimeter in tissue.
g Gamma rays are electromagnetic radiation similar to X-rays. Unlike the latter, which are produced by machines, gamma rays are emitted from the nucleus of a radioactive atom that is in an excited state. Gamma rays travel at the speed of light and can penetrate long distances in air and tissue. Several centimeters of lead or meters of water are needed to stop typical gamma rays
a decay
- involves strong and coloumbic forces- alpha particle and daughter nucleus have equal and opposite momentums
(i.e. daughter experiences “recoil”)
241 237 495 93 2Am Np Hea
decay - three types
- converts one neutron into a proton and electron- no change of A, but different element- release of anti-neutrino (no charge, no mass)
1) - decay
2) + decay
3) Electron capture
3 31 2 eH He e
11 116 5 eC B e
- converts one proton into a neutron and electron- no change of A, but different element- release of neutrino
7 74 3
ECeBe e B
g decay
- conversion of strong to coulombic E- no change of A or Z (element)- release of photon- usually occurs in conjunction with other decay
3 * 32 2He Heg g
Spontaneous fission
Fission tracks from 238U fission in old zircon
256 140 112100 54 46 4sfFm Xe Pd n
- heavy nuclides split into two daughtersand neutrons
- U most common (fission-track dating)
*Nuclear fission
*Half Life
*The time it takes for one half of the sample to decay
Activity calculations
- usually reported in dpm (disintegrations per minute), example: 14C activity = 13.56 dpm / gram C
Activity Nl
0tA A e l - because activity is linerarly proportional to number N,
then A can be substituted for N in the equation 0tN N e l
Example calculation:
How many 14C disintegrations have occurred in a 1g wood sample formed in 1804AD?
T=200y
t1/2 = 5730y so l = 0.693/5730y = 1.209e-4 y-1
N0=A0/l so N0=(13.56dpm*60m/hr*24hr/day*365days/y) /1.209e-4= 5.90e10 atoms
N(14C)=N(14C)0*e-(1.209e-4/y)*200y = 5.76e10 atoms
# decays = N0-N = 2.4e9 decays
* Heisenberg’s uncertainty Principle
*Models of the Atom
a Historical Perspective
Aristotle
*Early Greek Theories* 400 B.C. - Democritus thought matter could not be
divided indefinitely.
• 350 B.C - Aristotle modified an earlier theory that matter was made of four “elements”: earth, fire, water, air.
Democritus
• Aristotle was wrong. However, his theory persisted for 2000 years.
fire
air
water
earth
• This led to the idea of atoms in a void.
*John Dalton* 1800 -Dalton proposed a modern atomic model
based on experimentation not on pure reason.
• All matter is made of atoms.• Atoms of an element are identical.• Each element has different atoms.• Atoms of different elements combine
in constant ratios to form compounds.• Atoms are rearranged in reactions.
• His ideas account for the law of conservation of mass (atoms are neither created nor destroyed) and the law of constant composition (elements combine in fixed ratios).
*Adding Electrons to the Model
1)Dalton’s “Billiard ball” model (1800-1900)Atoms are solid and indivisible.
2) Thompson “Plum pudding” model (1900)Negative electrons in a positive framework.
3) The Rutherford model (around 1910)Atoms are mostly empty space.Negative electrons orbit a positive nucleus.
Materials, when rubbed, can develop a charge difference. This electricity is called “cathode rays” when passed through an evacuated tube (demos). These rays have a small mass and are negative.Thompson noted that these negative subatomic particles were a fundamental part of all atoms.
Ernest RutherfordRutherford shot alpha (a) particles at gold foil.
Most particles passed through. So, atoms are mostly empty.
Some positive a-particles deflected or bounced back!
Thus, a “nucleus” is positive & holds most of an atom’s mass.
Radioactive substance path of invisible a-
particles
Lead block
Zinc sulfide screen Thin gold foil
Bohr’s model
There are 2 types of spectra: continuous spectra & line spectra. It’s when electrons fall back down that they release a photon. These jumps down from “shell” to “shell” account for the line spectra seen in gas discharge tubes (through spectroscopes).
• Electrons orbit the nucleus in “shells”•Electrons can be bumped up to a higher shell if hit
by an electron or a photon of light.
*Quantum Model
*Quantum Numbers:*n = principal quantum number**l = azimuthal quantum number*(orbital angular momentum)
*ml = magnetic quantum number
*ms = spin magnetic quantum number
Orbitals and Quantum Numbers
Quantum Mechanics and Atomic Orbitals
The s-Orbitals
Representations of Orbitals
The p-Orbitals
Representations of Orbitals
d-orbitals
Electron Spin and the Pauli Exclusion Principle
Many-Electron Atoms
The smallest pieces of matter…• Nuclear physics
and particle physics study the smallest known building blocks of the physical universe -- and the interactions between them.
• The focus is on single particles or small groups of particles, not the billions of atoms or molecules making up an entire planet or star.
Further layers of substructure:
If each proton were 10 cm across, each quark would be .1 mm in size and the whole atom would be 10 km wide.
www.cpepweb.org
u quark: electric charge = 2/3
d quark: electric charge = -1/3
Proton = uud electric charge = 1
Neutron = udd electric charge = 0
Introducing the neutrino Another subatomic
particle, the neutrino, plays a crucial role in radioactive decays like n -> p+ + e- + veThe ve (electron-neutrino) is closely related to the electron but has
strikingly different properties.
Name Mass Electric Charge
electron 0.0005 GeV -1electron-neutrino < 0.00000001 GeV 0
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