1) The average threshold of dark-adapted vision is 4.00x10-11 W/m2 at a wavelength of 500nm.
a) What is the energy of one photon of this color of light?

b) The average maximum diameter of the pupil (in the dark) is 8.50 mm. How many Joules per second arrive through the pupil in the dark at the threshold level?

c) How many photons arrive through the pupil in the dark at the threshold level?

2) The metal in a photocell has a work function of 4.7eV. What is the maximum wavelength that will cause electrons to flow in the photocell?

3) Suppose an electron and a basketball have the same velocity of 10 m/s.
a) What is the DeBroglie wavelength of the electron? (mass = 9.1x10-31kg)

b) What is the DeBroglie wavelength of the basketball? (mass = 0.3kg)

c) Why do we see diffraction when an electron goes through a small opening but we do not see basketball diffraction when a basketball goes through the hoop?

4) You fall through a worm hole one day into a parallel universe where Planck's constant is 1 Js instead of its normal value.
a) What would be the basketball's DeBroglie wavelength for the same mass and velocity above?

b) Suppose the basketball undergoes single slit diffraction just like photons do and Plank's constant is 1 Js. If the hoop has an opening of 0.34m and is 3.3m above the floor, how far from directly under the goal is the first basketball maximum?

c) Suppose we put the basketball into a storeroom of width 2m. What is the uncertainty of its velocity while it is in the storeroom (h is still 1 Js)?

d) What would be the uncertainty in velocity of the basketball in the same storeroom if Planck's constant reverts to the true value?
5) The wave function of an electron in a one dimensional box is given by n = ˆ(2/L) sin (n¼x/L) where L is the width of the box and n = 1, 2, 3 .... Suppose the box has a width of L and has one edge at x = 0.
a) Sketch a graph of the probability as a function of x for the n = 3 state.

b) Make a list of the physical properties of an electron that can be calculated from the wave function (we talked about four of these in class last Thursday).

6) In a Helium-Neon laser electrons fall from an energy level of -20.66eV to a level of -22.62eV.
a) What frequency of photon is given off?

b) What is the wavelength of this photon?

7) The energy levels for hydrogen are given by En=13.6 eV/n2 . When hydrogen is placed into a magnetic field the energy levels split (this is called the Zeeman effect) and are increased (or decreased) by U = B ml where is given above, B is the magnetic field strength in Tesla and ml is the magnetic quantum number (ml= -l, -l +1, ... l-1, l). So The new energy levels are given by E = En ± U.
a) If the n = 3 level is split, ml = -1, 0, and 1 so the n = 3 level is split into three. What are the energies of these three levels if B = 50T?

b) What wavelength of photon will be given off if the electron drops from the n = 3, ml = 2 case in a magnetic field to the n = 2 level ml = 0 (which is not split)?

c) How does this compare with the original photon given off without the magnetic field (from the n = 3 to the n = 2 level)?

BONUS:
What is the difference between discrete radiation and Black Body radiation?

Explain the exclusion principle in terms of wave functions.

Explain how a laser works in terms of spontaneous and stimulated emission