Question

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

• A. (\frac{3}{2} \lambda_{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)