Modern PhysicsQuestions taken from/inspired by “Modern Physics” by Bernstein, Fishbane and Gasiorowicz

1. The ionization energy of He is 24.6 eV, and Li is 5.4 eV. What is the effective nuclear charge (Zeff) of these elements?

2. What is the Auger effect?

3. As a result of the evolutionary history of the universe, it has a background of blackbody radiation in all directions whose characteristic temperature is 2.7 K. This radiation distribution has a maximum at a certain frequency. Suppose a certain molecule has two levels whose energies differ by an amount corresponding to that energy. What is the maximum frequency and corresponding energy? You may want to use the Wien displacement law.

4. Consider a He-Ne gas laser with a wavelength of 633 nm. Use the equation for the wavelength of standing waves to calculate the n-value for a standing wave in a cylindrical cavity 80 cm long. Given that the spread in frequencies (Δf) of the neon atoms at room temperature is 1.7 E 9 Hz, what is the range of n-values covered by Δf?

5. In at experiment with a sample of a radioactive isomer, 10% of the original material is found to have decayed by a specific decay mode after exactly one week. What is the lifetime for this particular mode of decay? How much time will pass after the beginning of the experiment before 50% of the original amount will have decayed?

6. Show that the lifetime (τ) of a radioactive material is related to the half-life (τ1/2) by the equation τ1/2=ln(2) τ.

7. A nucleus decays into two channels with probabilities 0.62 and 0.38, respectively. Its lifetime is 20 hours. What are the decay rates into each of the two channels?

8. The angular spread of a laser beam is ideally diffraction limited; that is, the angular spread is given by ΔΘ = 1.22 λ/D, where λ is the wavelength of the light and D is the diameter of the aperture of the source—the diameter of the laser rod. What is the size of a spot projected by the beam at a distance of 1 km for a ruby laser (λ = 700 nm) with diameter 1 cm? If the beam has a flux corresponding to 10^18 photons emitted per second, what is the energy deposited per square centimeter per second at a target 1 km away?

9. What is a conduction band?

10. What are the more common names for “p carriers” and “n carriers”?

11. In the space between the arms of a galaxy, a gas composed of atomic hydrogen is present in the amounts of 0.5 atoms per cubic cm. Assuming atomic hydrogen acts like a

sphere of radius 1 angstrom insofar as its interactions with other atoms in the interstellar gas is concerned, what is the mean free path of a hydrogen atom in the gas?

12. A current of 1 A flows in copper wire 2 mm in diameter. The density of valence electrons in copper is roughly 9 x 10^28 per cubic meter. Find the drift speed of these electrons.

13. What is the Meissner effect?

14. Over what range (approximately) can nuclear forces be felt? How does this compare to the size of a proton or neutron?

15. Alpha decay occurs when an alpha particle tunnels from the nuclear potential well through the coulomb barrier. If the outer edge of the potential barrier (b) then obeys the condition that V(b) = VE (where VE is the electric potential), express b as a function of VE. Be sure to take into account that the alpha particle feels an effective nuclear charge and that the protons in the alpha particle do not contribute to Zeff.

16. What minimum or maximum value must the reproduction factor have in order to maintain a sustained fission chain reaction?

17. Why do charged pions have lifetimes that are so much (about 11 orders of magnitude) longer than neutral pions?

18. What particles carry the strong and weak nuclear forces? Why are gluons able to scatter directly off other gluons, while photons do not scatter off other photons? What is the difference between a vector boson and a scalar boson?

19. An electron revolves in a circle around a nucleus with positive charge Ze. How is the electron’s velocity related to the radius of its orbit?

20. A gas of monoatomic hydrogen is bombarded with a stream of electrons that have been accelerated from rest through a potential different of 12.75 V. Which spectral lines should be emitted?

21. What is a phonon?