Modern Physics Important Concepts for AP Test
Special Relativity
 Laws of Physics are same in all inertial reference frames
 Speed of light is the same regardless of velocity of observer or source of light
Followed results of Michelson-Morley Experiment – null result, ether does not exist and
velocity of light independent of velocity of earth
Absolute length and absolute time intervals are meaningless. Simultaneity of two events
is not an absolute concept but depends on the motion of the observer.
Moving clocks run more slowly. (time dilation)
Proper length is the longest length. (length contraction)
Energy and Relativistic Momentum (equations which may be used in problem section)
 Rest Energy (particle at rest still has energy associated with its mass)
 Erest = mc2
 Energy of photons (massless)
 E = pc
Total Energy E = K + mc2
Pair Production and annihilation
 Process in which a photon creates matter.
 An electron and positron (positively charged particle with mass of an electron) are
produced and the photon disappears.
 Energy, momentum, and charge must be conserved in this process.
 Ephoton = Eparticles produced hfmin = 2mec2 (x2 since there are 2 particles)
 Pair annihilation occurs when an electron-positron pair combine, disappear, and
create 2 photons (must create 2 for conservation of momentum).
Planck’s Hypothesis – Energy is quantized.
 Resonators are only allowed to have certain discrete energies (quantized), En,
given by En = nhf, where n is the quantum number an integer and h is Planck’s
constant.
 Used classical physics ultraviolet catastrophe in blackbody radiation.
Experimental data fit Planck’s hypothesis.
Light has a dual nature. It exhibits both wave and particle characteristics.
 Wave nature shown by interference and diffraction effects.
 Particle (quantum) nature shown in photoelectric effect and the Compton effect.
 Know the equations for photoelectric effect and how to use them (common
problem on AP test)
Wave Properties of Particles – deBroglie Wavelength
 deBroglie postulated that matter waves have frequencies that obey the relationship
E = hf
 photon equations
o E = hf = (hc)/λ
o p = E/c = h/ λ
 Matter equations (Matter does not move at c, do not use c = λּ f)
o deBroglie Wavelength λ = h/p = h/(mv) (Common problem on exam)
o f = E/h frequency of matter waves
 Davisson Germer Experiment measured wavelength of electrons. (wave
properties of matter)
o First experimental confirmation of matter waves proposed by deBroglie
 Heisenberg Uncertainty Principle – It is impossible to measure simultaneously
the exact position and exact linear momentum of a particle.
Atomic Physics
 Models of Atom
o J.J. Thomson “plum pudding” model
o Rutherford’s experiment found most matter concentrated in nucleus
proposed planetary type atomic model
o Bohr Model of Hydrogen
 Electrons exist only in certain allowed orbits determined by
integer, n. (quantized energy levels)
 Bohr radius = 0.0529 nm (Use for # atoms on head of pin in MC)
 En = -13.6/n2 eV (energy for quantum states of hydrogen)
o Atomic Transitions
 Electrons can absorb equal to the energy separation, ΔE, to move
from the ground state to an excited state (higher energy level).
 When electron jumps back to a lower level it emits a photon of
energy, ΔE. The wavelength is found using ΔE = hf. (Another
commonly asked problem on AP test.)
o Quantum Numbers
 The allowed orbital states for an electron in all atoms are specified
by 4 quantum numbers.
 Pauli Exclusion Principle –No two electrons in an atom can be in
the same quantum state. Each electron in a particular atom has a
unique set of 4 quantum numbers. This limits the number of
electrons found in any energy state.
Nuclear Physics
 ZA X represents element and nuclear particles as follows:
o X represents the chemical symbol for the element
o A represents the mass number the number of nucleons in the nucleus.
o Z represents the number of protons in the nucleus
o N represents the number of neutrons in the nucleus N = A – Z
o Isotopes of an element have the same Z number but different A and N
values.
 Radioactivity
o Know that half of radioactive nuclei in a given sample of material decays
for every half life of time that elapses.
o N = Noe- λt
o Decay Processes
 Alpha decay – nucleus emits an alpha particle ( 24 He ). Z and A
decrease by 2 each, X changes to appropriate element. Mass is not
conserved it is converted into energy in the decay process. Charge
and momentum are conserved.
 Beta Decay – nucleus emits particle, either an electron or
positron. Charge and momentum are conserved. A remains the
same but Z increases (electron) or decreases (positron) by 1.
 Gamma Decay – emission of a photon (gamma ray) when a
nucleus in an excited state returns to a lower energy state. Gamma
emission does not result in any change in either Z or A.