We know that the Sun is fundamental source of all energy that we use. Huge amount of energy is being produced in the Sun and this energy is radiated all around in the form of electromagnetic waves of several possible wavelengths. We can treat the Sun as a point source because it radiates energy uniformly in all directions. Intensity of wave at a point is defined as amount of energy passing that point per unit time and per unit area. We know that Earth is at a distance approximately `1.5 xx 10^(11)` m from the Sun and assume that intensity of radiation of the Sun reaching Earth's surface is `10^3` W/`m^2`.
How much energy is being radiated by the sun in one second ?

Options

A. `2.8 xx 10^(26) J`
B. `5.6 xx 10^(26) J`
C. `2.8 xx 10 ^(22) J`
D. `5.6 xx 10^(22) J`

Explanation

To find out how much energy is being radiated by the Sun in one second, we can use the relationship between intensity, power, and the distance from the Sun to the Earth.

### Step-by-step Solution:

1. **Understand the Definitions**:
- Intensity (I) is defined as the power (P) per unit area (A). Mathematically, it can be expressed as:
\[ I = \frac{P}{A} \]
- For a point source like the Sun radiating uniformly in all directions, the area (A) over which the power is spread at a distance \( r \) is the surface area of a sphere:
\[ A = 4\pi r^2 \]

2. **Given Values**:
- Distance from the Sun to the Earth, \( r = 1.5 \times 10^{11} \) m
- Intensity of radiation at Earth's surface, \( I = 10^3 \) W/m²

3. **Calculate the Area**:
- Substitute the value of \( r \) into the area formula:
\[ A = 4\pi (1.5 \times 10^{11})^2 \]

4. **Calculate the Power**:
- Rearranging the intensity formula gives us:
\[ P = I \times A \]
- Substitute the values of \( I \) and \( A \) to find the power radiated by the Sun:
\[ P = 10^3 \times 4\pi (1.5 \times 10^{11})^2 \]

5. **Perform the Calculations**:
- First, calculate \( (1.5 \times 10^{11})^2 \):
\[ (1.5 \times 10^{11})^2 = 2.25 \times 10^{22} \]
- Now calculate the area:
\[ A = 4\pi (2.25 \times 10^{22}) \approx 4 \times 3.14 \times 2.25 \times 10^{22} \approx 28.26 \times 10^{22} \text{ m}^2 \]
- Now calculate the power:
\[ P = 10^3 \times 28.26 \times 10^{22} \approx 2.826 \times 10^{25} \text{ W} \]

6. **Energy Radiated in One Second**:
- Since power is energy per unit time, the energy radiated by the Sun in one second is equal to the power:
\[ E = P \approx 2.826 \times 10^{25} \text{ J} \]

### Final Answer:
The energy being radiated by the Sun in one second is approximately \( 2.826 \times 10^{25} \) Joules.

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