Discussion
In an allowed band of semiconductor the effective mass m* of the electron is infinite :
Answer: C
The effective mass is infinite in the middle of the energy band.
The effective mass is set by the curvature of the band, \( \frac{1}{m^{*}} = \frac{1}{\hbar^{2}}\frac{d^{2}E}{dk^{2}} \). Near the bottom of a band \( E(k) \) curves upward and \( m^{*} \) is positive; near the top it curves downward and \( m^{*} \) is negative. In between there is an inflection point where the curvature is zero, so \( m^{*} \) becomes infinite: an applied force there produces no acceleration.
So it is finite (positive) at the bottom, finite (negative) at the top, and 'never' is wrong because every band has such an inflection point.
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