Discussion
Consider the energy E in the Brillouin zone as a function of the magnitude of the wave vector \(\vec{k}\) for a crystal of lattice constant 'a'. Then :
Answer: A
The correct statement is that the slope of E versus k is proportional to the group velocity.
The velocity of an electron wave packet in a band is the group velocity
\[ v_{g} = \frac{1}{\hbar}\frac{dE}{dk} \]
so the slope of the E-k curve is \(\hbar v_{g}\).
At the zone boundary \(|k| = \pi/a\) Bragg reflection produces standing waves and the slope is zero, not maximum. The curve is parabolic only near the band edges, where the effective mass approximation holds, not across the whole zone. The slope is also zero at k = 0, so it is not non-zero everywhere in the interval.
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