The sun radiates electromagnetic energy at the rate of `3.9xx10^(26)W`. Its radius is `6.96xx10^(8)m`. The intensity of sun light at the solar surface will be (in `W//m^(2)`)

Options

A. `1.4xx10^(4)`
B. `2.8xx10^(5)`
C. `64xx10^(6)`
D. `5.6xx10^(7)`

Explanation

To find the intensity of sunlight at the solar surface, we can use the formula for intensity \( I \):

\[ I = \frac{P}{A} \]

where \( P \) is the power radiated by the sun and \( A \) is the surface area over which this power is distributed. The surface area \( A \) of a sphere is given by:

\[ A = 4\pi r^2 \]

### Step 1: Identify the given values
- Power radiated by the sun, \( P = 3.9 \times 10^{26} \, \text{W} \)
- Radius of the sun, \( r = 6.96 \times 10^{8} \, \text{m} \)

### Step 2: Calculate the surface area of the sun
Using the formula for the surface area of a sphere:

\[ A = 4\pi r^2 \]

Substituting the value of \( r \):

\[ A = 4\pi (6.96 \times 10^{8})^2 \]

Calculating \( r^2 \):

\[ (6.96 \times 10^{8})^2 = 4.846016 \times 10^{17} \, \text{m}^2 \]

Now substituting this back into the area formula:

\[ A = 4\pi (4.846016 \times 10^{17}) \approx 4 \times 3.14 \times 4.846016 \times 10^{17} \]

Calculating \( 4 \times 3.14 \approx 12.56 \):

\[ A \approx 12.56 \times 4.846016 \times 10^{17} \approx 6.086 \times 10^{18} \, \text{m}^2 \]

### Step 3: Calculate the intensity
Now we can calculate the intensity \( I \):

\[ I = \frac{P}{A} = \frac{3.9 \times 10^{26}}{6.086 \times 10^{18}} \]

Calculating this gives:

\[ I \approx 6.4 \times 10^{7} \, \text{W/m}^2 \]

### Final Answer
The intensity of sunlight at the solar surface is approximately:

\[ I \approx 6.4 \times 10^{7} \, \text{W/m}^2 \]

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