The sun radiates maximum energy at wavelength `4753Å`. The surface temperature of the sun if `b=2.888xx10^(-3)mK`, is

Options

A. 6076 K
B. 5706 K
C. 4560 K
D. 7000K

Answer

To find the surface temperature of the sun using the given wavelength at which it radiates maximum energy, we can use Wien's Displacement Law. According to this law, the product of the wavelength at which the maximum radiation occurs (λ_max) and the absolute temperature (T) of the black body is a constant. The formula is given by:

\[ T = \frac{b}{\lambda_{\text{max}}} \]

where:
- \( T \) is the absolute temperature in Kelvin,
- \( b \) is Wien's displacement constant, approximately \( 2.888 \times 10^{-3} \, \text{m} \cdot \text{K} \),
- \( \lambda_{\text{max}} \) is the wavelength in meters.

### Step-by-step Solution:

1. **Convert the Wavelength to Meters:**
The given wavelength is \( 4753 \, \text{Å} \). We need to convert this to meters.
\[ \lambda_{\text{max}} = 4753 \, \text{Å} = 4753 \times 10^{-10} \, \text{m} \]

2. **Substitute the Values into the Formula:**
Now, we can substitute the values of \( b \) and \( \lambda_{\text{max}} \) into the formula for temperature.
\[ T = \frac{b}{\lambda_{\text{max}}} = \frac{2.888 \times 10^{-3} \, \text{m} \cdot \text{K}}{4753 \times 10^{-10} \, \text{m}} \]

3. **Calculate the Temperature:**
Performing the calculation:
\[ T = \frac{2.888 \times 10^{-3}}{4753 \times 10^{-10}} \approx 6076 \, \text{K} \]

4. **Conclusion:**
The surface temperature of the sun is approximately \( 6076 \, \text{K} \).