Question

Two stars A and B radiate maximum energy at wavelength \(3.9\times 10^{-7}\) m and \(5.2\times 10^{-7}\) m respectively. The ratio of the temperature of star A to that of star B will be

• A. \(2:3\)
• B. \(3:2\)
• C. \(3:4\)
• D. \(4:3\)

Hint:

Wien displacement law: wavelength of peak emission times temperature is constant.

Answer 1

The Correct Option is D

Step 1: Approach
Compare through the product $\lambda_mT$.

Step 2: Product
$\lambda_AT_A=\lambda_BT_B=b$. Then $T_A=\dfrac b{3.9\times10^{-7}}$ and $T_B=\dfrac b{5.2\times10^{-7}}$.

Step 3: Divide
$\dfrac{T_A}{T_B}=\dfrac{5.2}{3.9}=1.333=\dfrac43$.

Step 4: Answer
The ratio is $4:3$, option (D).

Final Answer:
The temperature ratio equals the inverse wavelength ratio, 5.2 over 3.9, which is 4 to 3, option (D). \[ \boxed{4:3} \]