5. Calculate the Fermi Energy for lead. [eV]
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- 15 b. Suppose an electron is in a spin state given by x = A(). 8i Find i. the normalization constant A ii. (S.) iii. (S.) and iv. the probability that a measurement of S, will yield h/2.4. Show that the internal energy, U, of an Einstein crystal is given by: 3Nhv 3Nhvexp(-ßhv) 2 1-exp(-Bhv) + U = Hint: The following identity will avoid you having to use the chain rule: d In(1− ef(x)) = −(ƒ'(x)) e²“ dx 1-e28 2. Calculate the Fermi energy for the valence electrons in sodium metal given that the valency of sodium is one, the density of sodium is 0.97 g cm-3, the mass of the electron is 9.05 × 10-²8 g, Planck's constant is 6.62 x 10-27 erg sec, Avogadro's number is 6-025 × 10²³ per gramme molecule and the atomic weight of sodium metal is 23. (Ans: €(0) = 3-12 eV, T≈ 37,000°K.) 73
- 7. For the 3p and 3d states of hydrogen, show that (-) avg =1/1290. ao. n²8. How does BCS theory explain the origin of bandgap and critical temperature in superconductors?1. Differentiate the three quantum numbers for an electron in the hydrogen atom and justify why the idea of an electron orbiting a proton has been abandoned.