1. The wavelength spectrum of the radiation energy emitted from a system in thermal equilibrium is observed to have a maximum value which decreases with increas¬ing temperature. Outline briefly the significance of this observation for quantum physics.
2. The "stopping potential" in a photoelectric cell depends only on the frequency v of the incident electromagnetic radiation and not on its intensity. Explain how the assumption that each photoelectron is emitted following the absorption of a single quantum of energy by is consistent with this observation.
3. Write down the de Broglie equations relating the momentum and energy of a free particle to, respectively, the wave number k and angular frequency w of the wave-function which describes the particle.
4. Estimate the momentum necessary for a beam of neutrons to resolve the structure within a crystal lattice of inter-atomic spacing 0.28 nm.
5. Write down the Heisenberg Uncertainty Principle as it applies to the position x and momentum p of a particle moving in one dimension.
6. Estimate the minimum range of momentwn of a quark confined inside a proton of size 10-15 m.
7. Explain briefly how the concept of wave-particle duality and the introduction of a wave packet for a particle satisfies the Uncertainty Principle.
8. Explain what is meant by quantum mechanical tunnelling through a potential en¬ergy barrier. Give two examples of physical phenomena which are attributable to such tunnelling.
9. Write down the two equations which govern the quantisation of the magnitude and z-component, respectively, of angular momentum in quantum physics. What values of the associated quantum numbers are allowed?
10. Describe briefly an experimental observation which demonstrates that an intrinsic angular momentum, or spin, can be assigned to an electron.
11. Explain what is meant by the degeneracy of a quantised energy level.
12. In a many electron atom, how many electrons can occupy the 3p, 4s, and 4d sub-shells, respectively?
13. Briefly explain the physical origin of fine structure in atomic spectra.
14. Briefly explain the physical origin of hyperfine structure in atomic spectra and hence the origin of the "21 cm wavelength" used in observational radio-astronomy.