\prob{97}
Lattice forces affect the motion of electrons in a metallic crystal, so that the relationship between the energy E and the wave number k is not the classical equation  , where m is the electron mass. Instead, it is possible to use an effective mass  given which of the following?
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$)
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}$)
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^{1/3}$)
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$)
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Advanced Topics }Solid State Physics
This is a result one remembers by heart from a decent solid state physics course. It has to do with band gaps, which is basically the core of such a course.
Then again, one can easily derive it from scratch upon recalling some basic principles: =\hbar^2 k^2/(2m)) ,  , where k is the wave vector, E is the energy, m is the mass, and p is the momentum.
From the above, one has  .
Set the two  's equal to get  . Cancel out the  's to get ) , after differentiating with respect to k on both sides.
Alternatively, one can try it Kittel's way:
Start with  . Then, = \hbar^{-1}(d^2E/dt^2F/\hbar)) . Thus, the effective mass is defined by  dv_g/dt=mdv_g/dt) .
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