Question

The wavelength of body radiation having maximum energy is $ \lambda_m $ at temperature $ T $. If the wavelength of radiation corresponds to maximum energy is $ \frac{\lambda}{3} $, then temperature is:

• A. \( 3T \)
• B. \( \frac{T}{3} \)
• C. \( 9T \)
• D. \( \frac{T}{9} \)

Hint:

Wien's displacement law helps us understand the relationship between the wavelength of maximum radiation and the temperature of the object emitting the radiation.

Answer 1

The Correct Option is A

We use Wien's displacement law, which states that the wavelength \( \lambda_m \) corresponding to the maximum energy of the radiation is inversely proportional to the temperature: \[ \lambda_m T = \text{constant} \] Given that the wavelength of radiation corresponding to maximum energy is \( \frac{\lambda_m}{3} \), we can set up the equation: \[ \frac{\lambda_m}{3} \times T_2 = \lambda_m \times T \] Simplifying: \[ \frac{T_2}{3} = T \] \[ T_2 = 3T \]
Thus, the temperature \( T_2 \) is three times the original temperature \( T \), making the correct answer \( 3T \).