Question

What is the maximum wavelength of EM radiation required to move an electron from the valence band to conduction band of a semiconductor? [Given: Energy gap \( E_g = 1.98 \times 10^{-19} \, J \); Planck's constant \( h = 6.6 \times 10^{-34} \, Js \)]

• A. \( 10^{-9} \, m \)
• B. \( 10^{-6} \, m \)
• C. \( 10^{-10} \, m \)
• D. \( 10^{-12} \, m \)

Hint:

Maximum wavelength corresponds to minimum energy required (band gap energy).

Answer 1

The Correct Option is B

Step 1: Energy of photon.
\[ E = \frac{hc}{\lambda} \]

Step 2: For minimum energy required.
\[ E = E_g \]

Step 3: Rearranging for wavelength.
\[ \lambda = \frac{hc}{E_g} \]

Step 4: Substitute values.
\[ \lambda = \frac{6.6 \times 10^{-34} \times 3 \times 10^8}{1.98 \times 10^{-19}} \]

Step 5: Simplify numerator.
\[ = \frac{19.8 \times 10^{-26}}{1.98 \times 10^{-19}} \]

Step 6: Final calculation.
\[ \lambda = 10^{-6} \, m \]

Step 7: Final Answer.
\[ \boxed{10^{-6} \, m} \]