Complex wave vectors in the energy gap find an expression for the imaginary part of the wave vector in the energy gap at the boundary of the first Brillouin zone, in the approximation that led to Eq. (46). Give the result for the Im (k) at the center of the energy gap. The result for small Im (k) is (h2/2m)[Im(k)]2 ≈ 2mU2/h2G2.

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substituting a hydrogen atom with a halogen in a hydrocarbon:

- the single bond remains single. a is wrong.

- the bond with hydrogen is as strong as with a halogen. c is wrong

- a hydrocarbon is saturated if there is no double bond. we do not know that so d is wrong.

- carbon will always have four valence electrons. e is wrong.

by elimination, the correct answer is b. the boiling point of the new compound increases.