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. `4.2xx10^6`
D. `6.4xx10^7`

Answer

To find the intensity of sunlight at the solar surface, we can use the formula for intensity, which relates power and area. The intensity \( I \) is given by the formula:

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

where \( P \) is the power radiated by the sun and \( A \) is the surface area over which the power is distributed.

1. **Identify the given values:**
- Power \( P = 3.9 \times 10^{26} \, \text{W} \)
- Radius of the sun \( R = 6.96 \times 10^{8} \, \text{m} \)

2. **Calculate the surface area of the sun:**
The surface area \( A \) of a sphere is given by the formula:
\[ A = 4 \pi R^2 \]
Plugging in the radius:
\[ A = 4 \pi (6.96 \times 10^{8})^2 \]

3. **Calculate \( R^2 \):**
\[ R^2 = (6.96 \times 10^{8})^2 = 4.8416 \times 10^{17} \, \text{m}^2 \]

4. **Calculate the surface area \( A \):**
\[ A = 4 \pi (4.8416 \times 10^{17}) \approx 4 \times 3.14 \times 4.8416 \times 10^{17} \approx 6.086 \times 10^{18} \, \text{m}^2 \]

5. **Substitute the values into the intensity formula:**
\[ I = \frac{P}{A} = \frac{3.9 \times 10^{26}}{6.086 \times 10^{18}} \]

6. **Perform the division:**
\[ I \approx 6.4 \times 10^{7} \, \text{W/m}^2 \]

Therefore, the intensity of sunlight at the solar surface is approximately \( 6.4 \times 10^{7} \, \text{W/m}^2 \).