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Chapter 5: Q31P (page 245)
Derive the Stefan-Boltzmann formula for the total energy density in blackbody radiation
Deriving the Stefan-Boltzmann formula for the total energy density in the blackbody radiation is
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(a)Use Equation5.113 to determine the energy density in the wavelength range. Hint: set, and solve for
(b)Derive the Wien displacement law for the wavelength at which the blackbody energy density is a maximum
You'll need to solve the transcendental equation, using a calculator (or a computer); get the numerical answer accurate to three significant digits.
(a) Using Equations 5.59 and 5.63, show that the wave function for a particle in the periodic delta-function potential can be written in the form
(b) There is an exception; At the top of a band where z is an integer multiple of yields .
Find the correct wave function for the case. Note what happens toeach delta function.
a) Hund鈥檚 first rule says that, consistent with the Pauli principle, the state with the highest total spin (S) will have the lowest energy. What would this predict in the case of the excited states of helium?
(b) Hund鈥檚 second rule says that, for a given spin, the state with the highest total orbital angular momentum (L) , consistent with overall antisymmetrization, will have the lowest energy. Why doesn鈥檛 carbon have? Note that the 鈥渢op of the ladder鈥�is symmetric.
(c) Hund鈥檚 third rule says that if a subshellis no more than half filled,
then the lowest energy level has; if it is more than half filled, thenhas the lowest energy. Use this to resolve the boron ambiguity inProblem 5.12(b).
(d) Use Hund鈥檚 rules, together with the fact that a symmetric spin state must go with an antisymmetric position state (and vice versa) to resolve the carbon and nitrogen ambiguities in Problem 5.12(b). Hint: Always go to the 鈥渢op of the ladder鈥� to figure out the symmetry of a state.
Imagine two noninteracting particles, each of mass m, in the infinite square well. If one is in the state(Equation 2.28 ), and the other in state , calculate localid="1658214464999" , assuming (a) they are distinguishable particles, (b) they are identical bosons, and (c) they are identical fermions.
Find the average energy per free electron , as a fraction of the
Fermi energy. Answer:
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