Question

The temperature of the surface of Sun is 6000 K. The wavelength corresponding to the maximum energy is nearly (Wien's constant, \( b = 2.89 \times 10^{-3} \, \text{mK} \))

• A. 1.82 \(\times 10^{-7}\) m
• B. 6.82 \(\times 10^{-7}\) m
• C. 5.32 \(\times 10^{-7}\) m
• D. 4.82 \(\times 10^{-7}\) m

Hint:

Use Wien's displacement law \( \lambda_{\text{max}} = \frac{b}{T} \) to find the wavelength of maximum energy emission. Ensure units are consistent and round appropriately.

Answer 1

The Correct Option is D

The wavelength corresponding to the maximum energy emitted by a black body is given by Wien's displacement law: \[ \lambda_{\text{max}} = \frac{b}{T} \] where:
- \( b = 2.89 \times 10^{-3} \, \text{mK} \) (Wien's constant),
- \( T = 6000 \, \text{K} \) (temperature of the Sun's surface).
Substitute the values: \[ \lambda_{\text{max}} = \frac{2.89 \times 10^{-3}}{6000} = 4.816 \times 10^{-7} \, \text{m} \] This is approximately \( 4.82 \times 10^{-7} \, \text{m} \). So, the wavelength corresponding to the maximum energy is 4.82 \(\times 10^{-7}\) m.

Answer 2

Step 1: Understand the problem
- Temperature of the Sun’s surface, \( T = 6000\,K \).
- Wien’s displacement constant, \( b = 2.89 \times 10^{-3} \, \text{mK} \).
- Find the wavelength \( \lambda_{\max} \) corresponding to maximum energy.

Step 2: Use Wien's displacement law
\[ \lambda_{\max} T = b \]

Step 3: Calculate \( \lambda_{\max} \)
\[ \lambda_{\max} = \frac{b}{T} = \frac{2.89 \times 10^{-3}}{6000} = 4.82 \times 10^{-7} \, \text{m} \]

Final answer:
The wavelength corresponding to maximum energy is \( 4.82 \times 10^{-7} \, \text{m} \).