Question

A black body has maximum wavelength \(\lambda_m\) at temperature \(2200\,\text{K}\). Its corresponding wavelength at temperature \(3300\,\text{K}\) will be

• A. \( \dfrac{9}{4}\lambda_m \)
• B. \( \dfrac{3}{2}\lambda_m \)
• C. \( \dfrac{4}{9}\lambda_m \)
• D. \( \dfrac{2}{3}\lambda_m \)

Hint:

According to Wien’s law, the peak wavelength is inversely proportional to absolute temperature.

Answer 1

The Correct Option is D

Step 1: Use Wien’s displacement law.
For a black body, \[ \lambda_{\max} T = \text{constant} \]

Step 2: Write relation for two temperatures.
\[ \lambda_m \times 2200 = \lambda' \times 3300 \]

Step 3: Solve for new wavelength.
\[ \lambda' = \lambda_m \frac{2200}{3300} = \frac{2}{3}\lambda_m \]