Physics 252 Final Review Sheet

The final will have six problems. A good way to prepare is to review the web notes, and be sure you know how to do all the homework assignments.

You need to know *by heart* the following:

Time dilation and length contraction formulas.

Lorentz transformations: *x*, *t* to *x*', *t*' and *E*, *p* to *E*', *p*'.

Addition of velocities formula.

Mass increase. Energy-momentum relationship.

Energy-mass equivalence.

Doppler shift for light.

Speed of light = 3 x 10^{8} meters per second

Avogadro's Number *N _{A}* = 6 x 10

(Remember, a mole is the molecular weight in *grams*, not kilograms)

Boltzmann's constant = 1.4 x 10^{-23} Joules/K

Planck's constant* h* = 6.6 x 10^{-34} Joule-sec

Electron mass = 9 x 10^{-31} kilograms

Electron charge = 1.6 x 10^{-19} coulombs

Topics to Review (besides Relativity)

*Kinetic Theory of gases*:

How to derive pressure from simple molecular picture.

There is on average an energy 1/2*kT* in each degree of freedom.

The probability of a molecule having energy *E* is proportional to e^{-E/kT}.

How this relates to Maxwell's distribution.

*Black body radiation*:

Simple ideas about light interacting with matter: transparency, reflection, etc.

Stefan's Law. (You don't need to memorize the constant)

Wein's displacement law. (Similarly)

*Know* the approximate wavelengths and frequencies for visible light.

State what was the "ultraviolet catastrophe", and how Planck resolved it.

Be able to sketch the black body curve and explain the low and high frequency parts.

*The Photoelectric Effect*:

Be able to describe Lenard's experiment (or a more recent version - just a standard photoelectric effect experiment, in other words), what is expected classically on changing light intensity and color, what is actually observed, and how this can be used to find Planck's constant.

How were the photoemitted particles identified?

*Rays and Particles*:

Be able to describe Thomson's measurement of *e*/*m* for cathode rays.

How x-rays were discovered, how their properties were found, how an x-ray tube can be used to find Planck's constant.

How radioactivity was discovered, approximately how much energy radium puts out, what are the alpha, beta and gamma rays, and how do we know?

*Thomson's model* *of the hydrogen atom:* and why the frequency of radiation emitted depended on the size of the atom.

*Rutherford's scattering experiment*, and why it implied the existence of a nucleus in atoms.

*Bohr's model of the hydrogen atom* should be thoroughly understood: why it explains the Balmer series. In particular, you should understand *why the correspondence principle fixes the unit of angular momentum quantization, *and hence the Rydberg constant.

*Electron waves*: read and understand the web notes. You must be familiar with the interpretation of the wave in terms of the probability of finding the particle at any point. Know by heart the de Broglie relations, how this explains Bohr's quantization, two-slit diffraction, the expression for e^{iq} in terms of cosq and sinq, the uncertainty relation. Have a qualitative grasp of how wave packets illustrate the uncertainty principle. Know how the uncertainty principle works in practice (such as looking at an electron with a microscope) and how it relates to minimum electron energies in a box, an atom, or any potential well.

*Schrödinger equation*: you should know the one-dimensional time-dependent and time-independent forms by heart, and the time varying factor that multiplies the solution of the time independent equation. Understand how a sum of two solutions with different time dependences can give a time varying probability distribution. Be able to solve the infinite square well, and be able to sketch the essential features of the wave function (approximate wavelength or exponential behavior, and amplitude) for various one-dimensional potentials: finite square well, step, simple harmonic oscillator, tunneling wave function. You should be able to describe qualitatively what the wavefunction looks like for a *two* dimensional harmonic oscillator. Know why the wave function must be smooth (for finite potential) and when it represents a bound state. You need to know the difference between *fermions and bosons*, and how the difference is reflected in the symmetry of the wave function, which particles are which, and how *Pauli's exclusion principle* works.

*Atomic physics*: memorize the allowed sets of quantum numbers in the hydrogen atom (*n*,*l*,*m*,spin) understand what each of them means physically, including spin, and be prepared to explain the first few elements of the periodic table in terms of electrons with these numbers.

Know how the *Stern-Gerlach* experiment proves the quantization of a component of angular momentum.

*Nuclear physics*: simple properties of nucleons, approximate range and strength of the nuclear force, for which ranges of *Z *and *A* nuclei are most stable and why, a and b radioactive decay, nuclear fission and fusion.