Question

A black body emits radiation of maximum intensity at wavelength '$\lambda$' at temperature $T$ K. Its corresponding wavelength at temperature $1.5 T$ K will be ______.

• A. $\frac{2\lambda}{3}$
• B. $\frac{4\lambda}{3}$
• C. $\frac{16\lambda}{81}$
• D. $\frac{81\lambda}{16}$

Hint:

Always ensure temperatures are in absolute Kelvin scale before applying Wien's Law. Inverse proportionality means if the temperature goes up by a factor of 1.5 ($3/2$), the wavelength must go down by that same factor (multiply by $2/3$).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Wien's Displacement Law states that the wavelength ($\lambda_m$) corresponding to maximum emission intensity is inversely proportional to the absolute temperature ($T$).

Step 2: Formula Application:
$\lambda_m T = \text{constant}$ or $\lambda_1 T_1 = \lambda_2 T_2$.

Step 3: Explanation:
Given $\lambda_1 = \lambda, T_1 = T$, and $T_2 = 1.5 T$. $\lambda \cdot T = \lambda_2 \cdot (1.5 T)$ $\lambda_2 = \frac{\lambda}{1.5} = \frac{\lambda}{3/2} = \frac{2\lambda}{3}$.

Step 4: Final Answer:
The corresponding wavelength is $2\lambda/3$.