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Chapter 10: Q50E (page 469)
Assuming an interatomic spacing of 0.15 nm, obtain a rough value for the width (in eV) of the band in a one-dimensional crystal.
The estimated value of the band width is .
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By the 鈥渧ector鈥� technique of example 10.1 , show that the angles between all lobes of the hybridstates are .
In the boron atom, the single electron does not completely fill any spatial state, yet solid boron is not a conductor. What might explain this? (It may be helpful to consider again why beryllium is not an insulator.)
The effective force constant of the molecular 鈥渟pring鈥� in HCL is , and the bond length is .
(a) Determine the energies of the two lowest-energy vibrational states.
(b) For these energies, determine the amplitude of vibration if the atoms could be treated as oscillating classical particles.
(c) For these energies, by what percentages does the atomic separation fluctuate?
(d) Calculate the classical vibrational frequencyand rotational frequency for the rotational frequency, assume that L is the its lowest non zero value, and that the moment of inertia is .
(e) Is is valid to treat the atomic separation as fixed for rotational motion while changing for vibrational?
Starting with equation (10-4), show that if is as a photon is emitted by a diatomic molecule in a transition among rotation-vibration states, but can be . Then the allowed photon energies obey equation (10-6).
Section 10.2 gives the energy and approximate proton separation of the molecule. What is the energy of the electron alone?
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