Question

The effective mass ($m^*$) of an electron when it moves is

• A. $m^* = \frac{\hbar^2}{\frac{d^2E}{dk^2}}$
• B. $m^* = \frac{2\hbar^2}{\frac{d^2E}{dk^2}}$
• C. $m^* = \frac{4\hbar^2}{\frac{d^2E}{dk^2}}$
• D. $m^* = \frac{6\hbar^2}{\frac{d^2E}{dk^2}}$

Hint:

The effective mass reflects how easily an electron accelerates under an electric field. Lower band curvature (d2E/dk2) results in a heavier effective mass.

Answer 1

The Correct Option is A

The effective mass $m^*$ of an electron is derived from the curvature of the energy band:
\[ m^* = \frac{\hbar^2}{\frac{d^2E}{dk^2}} \]
This equation signifies that the effective mass depends on the second derivative of the energy $E$ with respect to the wave vector $k$. It is inversely related to the curvature of the band.