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: Understanding the Concept
Wien's displacement law says \(\lambda_mT=b\), a constant. A hotter star radiates its peak energy at a shorter wavelength.

Step 2: Write for both stars
\[ \lambda_AT_A=\lambda_BT_B\Rightarrow\frac{T_A}{T_B}=\frac{\lambda_B}{\lambda_A} \]

Step 3: Substitute
\[ \frac{T_A}{T_B}=\frac{5.2\times10^{-7}}{3.9\times10^{-7}}=\frac{52}{39}=\frac43 \]

Step 4: Check the options
Star A has the shorter wavelength, so it is the hotter one and the ratio must be greater than 1. That rules out 2:3 and 3:4. The value 3:2 would need a wavelength ratio of 1.5, which does not match 5.2/3.9. So the answer 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). \[ \boxed{4:3} \]