Physics 222 Test 3 3/24/03 name____________________

1eV = 1.6x10^-19J h= 6.602x10^-34 Js sin q_m = ml/a for minima, m= ±1, ±2, ±3...

1) An FM radio transmitter has a power output of 150kW and operates at a frequency of 103MHz.

a) What is the energy of one photon of this signal?

b) How many photons per second are emitted by the transmitter?

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^{- 31}kg)

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 join Fuzzy the quantum duck one day in his pond in Quantum World where Planck's constant is 1 Js instead of its normal value.

a) What would be the DeBroglie wavelength for Fuzzy's basketball if it has the same mass and velocity as the one above above?

b) Suppose the basketball undergoes single slit diffraction just like photons do and Planck'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 should Fuzzy stand to be at the first basketball minimum?

5) The wave function of an electron in a one dimensional box is given by y_n = Ö(2/L) sin (npx/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.

c) Why do you only have one quantum number for this case but you get four quantum numbers for Dirac's solution for the electron in a hydrogen atom?

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?

7a) What is the experimental evidence supporting the idea that the electron can only have spin values of + or - 1/2?

b) List the four quantum numbers and tell what physical quantity each corresponds to (list everything you know).

c) What is quantum tunneling?

d) Explain the exclusion principle in terms of wave functions.

8a) The most stable chemical elements are the noble gasses. Why then does your book say that iron is the most stable nucleus?

b) How does carbon 14 dating work?

c) What is the difference between fission and fusion (and which elements on the periodic table are fuels for each process)?

BONUS:

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

Explain the significance of the Davisson Germer experiment.