Calculate the effective temperature of the sun . Given that the wavelength of maximum energy in the solar spectrum is 475 mm and Wien's constant is `2.898xx10^(-3)` mK.

Explanation

To calculate the effective temperature of the sun using Wien's displacement law, follow these steps:

### Step 1: Understand the Given Information
We are given:
- Wavelength of maximum energy (λm) = 475 nm = 475 × 10^(-9) m
- Wien's constant (B) = 2.898 × 10^(-3) m·K

### Step 2: Write Down Wien's Displacement Law
Wien's displacement law states that:
\[ \lambda_m \cdot T = B \]
Where:
- \( \lambda_m \) is the wavelength corresponding to maximum energy,
- \( T \) is the temperature in Kelvin,
- \( B \) is Wien's constant.

### Step 3: Rearrange the Formula to Solve for Temperature
To find the temperature \( T \), we can rearrange the formula:
\[ T = \frac{B}{\lambda_m} \]

### Step 4: Substitute the Values into the Formula
Now, substitute the known values into the equation:
\[ T = \frac{2.898 \times 10^{-3} \text{ m·K}}{475 \times 10^{-9} \text{ m}} \]

### Step 5: Perform the Calculation
Now, calculate the temperature:
1. Calculate the denominator:
\[ 475 \times 10^{-9} = 4.75 \times 10^{-7} \text{ m} \]
2. Now divide:
\[ T = \frac{2.898 \times 10^{-3}}{4.75 \times 10^{-7}} \]
\[ T \approx 6101.05 \text{ K} \]

### Step 6: Final Result
Thus, the effective temperature of the sun is approximately:
\[ T \approx 6101 \text{ K} \]

---