The spectral energy distribution of the sun (temperature = 6050 K ) has a maximum at `4753Å` The temperature of a star for which this maximum is at `9506 Å` is

Options

A. 6050 K
B. 3025 K
C. 12100 K
D. 24200 K

Answer

To solve the problem, we will use Wien's Law, which states that the product of the temperature (T) of a black body and the wavelength (λ) at which the emission is maximized is a constant (b). The formula is given by:

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

Where:
- \( \lambda_{\text{max}} \) is the wavelength at which the emission is maximum,
- \( T \) is the absolute temperature in Kelvin,
- \( b \) is Wien's displacement constant, approximately \( 2.898 \times 10^{-3} \, \text{m} \cdot \text{K} \).

### Step-by-Step Solution:

1. **Identify the known values for the Sun:**
- Wavelength for the Sun, \( \lambda_1 = 4753 \, \text{Å} = 4753 \times 10^{-10} \, \text{m} \)
- Temperature of the Sun, \( T_1 = 6050 \, \text{K} \)

2. **Calculate the constant \( b \) using the Sun's values:**
\[ b = \lambda_1 \cdot T_1 = (4753 \times 10^{-10} \, \text{m}) \cdot (6050 \, \text{K}) \]

3. **Calculate \( b \):**
\[ b \approx 2.874 \times 10^{-6} \, \text{m} \cdot \text{K} \]

4. **Identify the known values for the star:**
- Wavelength for the star, \( \lambda_2 = 9506 \, \text{Å} = 9506 \times 10^{-10} \, \text{m} \)

5. **Use Wien's Law to find the temperature of the star \( T_2 \):**
\[ \lambda_2 \cdot T_2 = b \]
Rearranging gives:
\[ T_2 = \frac{b}{\lambda_2} \]

6. **Substitute the values to find \( T_2 \):**
\[ T_2 = \frac{2.874 \times 10^{-6} \, \text{m} \cdot \text{K}}{9506 \times 10^{-10} \, \text{m}} \]

7. **Calculate \( T_2 \):**
\[ T_2 \approx 3025 \, \text{K} \]

### Final Answer:
The temperature of the star is approximately **3025 K**.