Modern Physics

Fall 2009

Assignment 6: Due Friday, November 6. (Revised)

1. In He⁺, singly ionized helium, there is one electron, two protons and two neutrons, so the atomic number Z is 2. What is the energy if the electron is in the second level, n=2?

2. What is the third energy level, n=3?

3. If the electron goes from the n=3 level to the n=2 level in singly ionized helium and emits a photon, what is the wavelength of the photon?

4. What is the n=1 energy level of an electron in iron? (Assume there is no screening of the nucleus by other electrons.)

5. What is the n=2 energy level of an electron in Iron

a) If there is no screening of the nucleus by the n=1 electrons?

b) If the screening of the nucleus by the n=1 electron effectively reduces Z by 1 for the iron nucleus.

6. If one if the n=1 levels was vacant in the iron atom above and one of the n=2 electrons made a transition to the n=1 level, what would be the energy and the wavelength of the photon emitted? (Use the energy from 5a.)

7. Consider the electronic transitions in singly ionized ³He from the n=4 to the n=3 level and the same transition in singly ionized ⁴He. What would you expect for the fractional difference in the wavelengths for the photon emitted in those two transitions? (I want Dl/l_o where l_o is the wavelength of the photon for the transition in ³He.) Use the reduced mass for electron’s mass, M_e, in both cases, or

8. Find the lowest two energy states in a muonium atom that consists of a proton and a muon. A muon has negative charge like the electron but a mass of 106MeV/c² compared to the electron’s mass of 0.511MeV/c².