Question

Arrange the following dispersion graphs in decreasing order of their corresponding effective electron mass.

• A. A \(>\) D \(>\) C \(>\) B
• B. A \(>\) B \(>\) C \(>\) D
• C. D \(>\) C \(>\) B \(>\) A
• D. B \(>\) C \(>\) A \(>\) D

Hint:

Flatter \(E-k\) curve means larger effective mass; sharper curvature means smaller effective mass.

Answer 1

The Correct Option is A

Concept:
Effective mass of an electron in a band is related to the curvature of the \(E-k\) dispersion curve. \[ m^*=\frac{\hbar^2}{\frac{d^2E}{dk^2}} \]

Step 1: Understand the relation.
Effective mass is inversely proportional to curvature. \[ m^*\propto \frac{1}{\text{curvature}} \]

Step 2: Compare graphs.
A flatter dispersion curve has smaller curvature and hence larger effective mass. A more sharply curved graph has larger curvature and hence smaller effective mass.

Step 3: Arrange according to decreasing effective mass.
From the given graphs, the order of decreasing effective mass is: \[ A>D>C>B \] \[ \therefore \text{Correct Answer is (A)} \]