1) 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 the small spacing of a crystal but we do not see basketball diffraction when a basketball goes through the hoop?

Suppose Planck's constant is 1 Js instead of its normal value for the next 2 parts:
d) What is the basketball's DeBroglie wavelength for the same mass and velocity above?

e) What implication would a value of h = 1Js have for a basketball game where the ball would be traveling through an opening approximately the same size as the ball's wavelength?

2) Schrodinger's equation for Helium gives solutions which are very similar to those for hydrogen but the energy levels of helium are given approximately by E =-13.6 Z2 eV/n2 where Z, the atomic number, equals 2 for helium.
a) What are the lowest five energy levels for helium?

b) If an electron makes a transition to the n = 2 energy level from n = 3, 4 and 5 levels, what wavelength of photon is given off in each case?

c) Which, if any, of these photons are in the visible range?

d) If the n = 2 level is split by the normal Zeeman effect, how many lines will there by once the magnetic field is applied?

d) What is the energy of each of the new levels if B = 50T? (U = „ B ml Careful, this formula gives the change in energy from the original n = 2 level; you will need to add this to the energy in part a to have the new energy levels.)

e) Explain the physical basis for the difference between the normal Zeeman effect and the anomalous Zeeman effect.

3) The wavefunction of an electron in a one dimensional box is given by 8n = 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 = 4.0 ao in units of ao and has one edge at x = 0.
a) Find the probability (in units of 1/ao) for finding the electron at the following points for the n = 1 state: x = L/4, L/2, L, 3L/4, L.

b) Sketch a graph of the probability as a function of x for this state (you may use your graphing calculator and show the instructor). Remember the box ends at x = L.

c) Repeat the sketch for the n = 2 state.

d) Why is Schrodinger's picture of the atom better than the Bohr model even though Schrodinger's model is mathematically more difficult?

d) Which quantum number is not given by Schrodinger's equation and why?

Bonus:
Why is Schrodinger's cat mentioned in these chapters?

How does a laser work?