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 Wien's Displacement Law, we can follow these steps:

### Step 1: Understand Wien's Displacement Law
Wien's Displacement Law states that the product of the wavelength at which the radiation is maximum (λ_max) and the absolute temperature (T) of a black body is a constant (B). Mathematically, it can be expressed as:
\[ \lambda_{max} \cdot T = B \]

### Step 2: Identify the Given Values
From the problem, we have:
- Wavelength at maximum energy, \( \lambda_{max} = 4753 \, \text{Å} \)
- Constant \( B = 2.888 \times 10^{-3} \, \text{m} \cdot \text{K} \)

### Step 3: Convert Wavelength to Meters
Since the constant B is given in meters, we need to convert the wavelength from angstroms to meters:
\[ 1 \, \text{Å} = 10^{-10} \, \text{m} \]
Thus,
\[ \lambda_{max} = 4753 \, \text{Å} = 4753 \times 10^{-10} \, \text{m} = 4.753 \times 10^{-7} \, \text{m} \]

### Step 4: Rearrange Wien's Displacement Law to Solve for Temperature
We can rearrange the equation to solve for the temperature (T):
\[ T = \frac{B}{\lambda_{max}} \]

### Step 5: Substitute the Values into the Equation
Now we substitute the values of B and λ_max into the equation:
\[ T = \frac{2.888 \times 10^{-3} \, \text{m} \cdot \text{K}}{4.753 \times 10^{-7} \, \text{m}} \]

### Step 6: Calculate the Temperature
Now we perform the calculation:
\[ T = \frac{2.888 \times 10^{-3}}{4.753 \times 10^{-7}} \]
\[ T \approx 6076 \, \text{K} \]

### Final Answer
The surface temperature of the sun is approximately \( 6076 \, \text{K} \).

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