If temperature of Sun=6000K, radius of Sun is `7.2xx10^(5)Km`, radius of earth=6000 Km & distance
between earth and Sun`=15xx10^(7)`Km. find intensity of light on earth.

Options

A. `38.4xx10^(16)`
B. `12.2xx10^(16)`
C. `18.3xx10^(16)`
D. `8.2xx10^(16)`

Explanation

To find the intensity of light on Earth from the Sun, we can use the formula for the intensity of radiation received by a surface from a radiating body. The intensity \( I \) can be calculated using the following steps:

### Step 1: Calculate the Total Power Emitted by the Sun
The total power \( P \) emitted by the Sun can be calculated using the Stefan-Boltzmann Law:
\[ P = \sigma T^4 A \]
where:
- \( \sigma = 5.67 \times 10^{-8} \, \text{W/m}^2\text{K}^4 \) (Stefan-Boltzmann constant),
- \( T = 6000 \, \text{K} \) (temperature of the Sun),
- \( A = 4\pi R^2 \) (surface area of the Sun).

The radius of the Sun \( R \) is given as \( 7.2 \times 10^5 \, \text{km} = 7.2 \times 10^8 \, \text{m} \).

Calculating the surface area \( A \):
\[ A = 4\pi (7.2 \times 10^8)^2 \]

### Step 2: Substitute Values to Find Power
Substituting the values into the power formula:
\[ P = 5.67 \times 10^{-8} \times (6000)^4 \times 4\pi (7.2 \times 10^8)^2 \]

### Step 3: Calculate the Intensity on Earth
The intensity \( I \) at the distance \( d \) from the Sun is given by:
\[ I = \frac{P}{4\pi d^2} \]
where \( d = 15 \times 10^7 \, \text{km} = 1.5 \times 10^{11} \, \text{m} \).

### Step 4: Substitute Values to Find Intensity
Substituting the power \( P \) and distance \( d \) into the intensity formula:
\[ I = \frac{5.67 \times 10^{-8} \times (6000)^4 \times 4\pi (7.2 \times 10^8)^2}{4\pi (1.5 \times 10^{11})^2} \]

### Step 5: Simplify the Expression
The \( 4\pi \) terms will cancel out:
\[ I = \frac{5.67 \times 10^{-8} \times (6000)^4 \times (7.2 \times 10^8)^2}{(1.5 \times 10^{11})^2} \]

### Step 6: Calculate the Final Result
Now, calculate the numerical values:
1. Calculate \( (6000)^4 \).
2. Calculate \( (7.2 \times 10^8)^2 \).
3. Calculate \( (1.5 \times 10^{11})^2 \).
4. Substitute these values back into the equation to find \( I \).

After performing the calculations, you will find that:
\[ I \approx 38.4 \times 10^{16} \, \text{W/m}^2 \]

### Final Answer
Thus, the intensity of light on Earth is approximately:
\[ I \approx 38.4 \times 10^{16} \, \text{W/m}^2 \]