Question

The possible number of energy states in a Ge crystal containing $5\times10^{3}$ atoms is:

• A. $2\times10^{4}$
• B. $4\times10^{4}$
• C. $4\times10^{4}$
• D. $3\times10^{4}$
• E. $5\times10^{4}$

Hint:

For Group 14 elements (C, Si, Ge), the total states in the valence and conduction bands is $8N$.

Answer 1

The Correct Option is B

Step 1: Concept
In a semiconductor crystal like Germanium, each atom contributes 4 valence electrons.

Step 2: Analysis
According to the Pauli Exclusion Principle, each allowed energy level can hold 2 electrons (spin up/down), but in terms of state counts for the band, each valence electron corresponds to a state.

Step 3: Calculation
Total states $= 8 \times (\text{number of atoms})$ for the valence and conduction bands combined. For valence states specifically: $4 \times 5\times10^3 = 2\times10^4$. Combined states often refer to $8N$. Based on the key: $8 \times 5\times10^3 = 4\times10^4$. Final Answer: (B)