Question

In a p-type semiconductor, the acceptor level is situated 50 meV above the valence band. The maximum wavelength of light required to produce a hole will be:

• A. $24.8 \times 10^{-5} \, \text{m} \\$
• B. $0.248 \times 10^{-5} \, \text{m} \\$
• C. $2.48 \times 10^{-5} \, \text{m} \\$
• D. $248 \times 10^{-5} \, \text{m}$

Answer 1

The Correct Option is C

Given:

Acceptor level = 50 meV above valence band

1 eV = 1.6 × 10⁻¹⁹ J

h = 6.63 × 10⁻³⁴ J·s

c = 3 × 10⁸ m/s

Energy required to create a hole:

\[ E = 50 \text{ meV} = 50 \times 10^{-3} \times 1.6 \times 10^{-19} \text{ J} \]

\[ E = 8 \times 10^{-21} \text{ J} \]

Maximum wavelength (λₘₐₓ):

\[ \lambda_{max} = \frac{hc}{E} \]

\[ \lambda_{max} = \frac{(6.63 \times 10^{-34})(3 \times 10^8)}{8 \times 10^{-21}} \]

\[ \lambda_{max} = 2.486 \times 10^{-5} \text{ m} \]

\[ \lambda_{max} \approx 2.48 \times 10^{-5} \text{ m} \]

Answer: The maximum wavelength is \(\boxed{2.48 \times 10^{-5} \text{ m}}\) (Option 3)

Answer 2

\(\text{ The energy required to produce a hole is } 50 \, \text{meV} = 50 \times 10^{-3} \, \text{eV} = 8.0 \times 10^{-21} \, \text{J}.\\\)
\(\text{The wavelength corresponding to this energy is given by:}\)
\(E = \frac{hc}{\lambda} \implies \lambda = \frac{hc}{E}\)

\(\text{Substitute } h = 6.626 \times 10^{-34} \, \text{J.s}, \, c = 3 \times 10^8 \, \text{m/s}, \text{ and } E = 8.0 \times 10^{-21} \, \text{J}:\)

\[\lambda = \frac{6.626 \times 10^{-34} \times 3 \times 10^8}{8.0 \times 10^{-21}} = 2.48 \times 10^{-5} \, \text{m}\]