Physics 325 Quiz 2 October 21, 2005

Open book and notes, calculator allowed. Show HOW you arrive at your answers. No credit for random scratch work on the page. If you cannot get it to work out, explain in words how you are going about it. M(electron)= 9.1 x 10 ^-31 kg.;

M(proton)= M(neutron)=1.67 x 10 ^-27 kg; M(m-meson)=207 x M(electron); h=6.6 x 10 ^-34 J-sec; 1 eV=1.6 x 10 ^-19 J; speed of light = 3 x 10 ⁸ m/s.

1. (20) An electron is confined to an infinite square well 1 nm wide.

a) If this electron starts in the second excited state of this well, what energy photons can be emitted as it returns to the ground state?

b) If the electron is in the second excited state of this well, what is the probability that a measurement of its position will find it in an interval 0.01 nm wide centered at the center of the well (the answer is not zero) ?

2. (40) An electron is emitted from a hot cathode and accelerated to an energy of 5 eV in such a way that its wave function is a wave packet 10^-3 mm long.

a) What are the deBroglie wavelength l and the wave number k for this electron?

b) If a beam of these electrons were sent through a pair of slits separated by 0.5 nm (think atoms in a crystal), how far apart would be the interference fringes on a screen located 20 cm downstream?

c) What is the uncertainty in k of this electron (i.e., Dk)?

d) What is the uncertainty in energy of this electron in eV?

3. (40) An x-ray tube is operated with an iron (Z=26) anode.

a) What does the term “K_a x-ray” mean?

b) What is the lowest voltage on the tube which will produce a K_a x ray from this anode?

c) What is the energy in eV of a K_a x ray from iron?

d) Why is this energy close to, but not equal to, the answer to part (b) (multiplied by the charge on the electron) ?

4. (40) a) In the Bohr model of the atom the energy is given by –E_o/n². Describe in a couple of sentences what n is and what assumption had to be made by Bohr to result in this quantization of the energy.

b) Take a Bohr model for one-electron argon (Z=17). Find the frequency of the lowest energy photon which could be emitted from such an atom if it started in the n=4 state.

c) Find the radius for the n=4 orbit.

d) Find the (classical) frequency of circulation of an electron in this orbit and compare it to your answer to part (b). Comment on the comparison.

5. Bonus: (10) Do this only if you are bored. In the homework you had a problem to model the nucleus of an atom as a proton moving in an infinite well 1 fm wide. Instead, make a Bohr model for the nucleus: suppose a nucleus of deuterium is made of a proton and a neutron orbiting each other at a separation of 1 fm. What would be the kinetic energy of the lowest state? Why is this not the entire energy of the state?