Question

A black body has maximum wavelength ' \(\lambda_{\mathrm{m}}\) ' at temperature 2000 K . Its maximum wavelength at 3000 K will be

• A. \(\frac{3}{2}\lambda _{\mathrm{m}}\)
• B. \(\frac{16}{81}\lambda _{m}\)
• C. \(\frac{81}{16}\lambda _{m}\)
• D. \(\frac{2}{3}\lambda _{m}\)

Hint:

Peak wavelength is inversely proportional to the absolute temperature.

Answer 1

The Correct Option is D

Step 1: Wien's Displacement Law
$\lambda_m T = \text{constant} \implies \lambda_1 T_1 = \lambda_2 T_2$.

Step 2: Calculation
$\lambda_m (2000) = \lambda_2 (3000)$.
$\lambda_2 = \frac{2000}{3000} \lambda_m = \frac{2}{3} \lambda_m$.
Final Answer: (D)