The intensity of the sun on the carth is `1500W/ m^2`. Assuming the earth to be a black body, calculate the adiation pressure in multiple of `10^(6) N /m^2`.

Answer

To calculate the radiation pressure on Earth due to the intensity of sunlight, we can use the following relationship:

**Step 1: Understand the relationship between intensity and radiation pressure.**
The radiation pressure \( P \) exerted by electromagnetic radiation can be calculated using the formula:
\[ P = \frac{I}{c} \]
where:
- \( P \) is the radiation pressure,
- \( I \) is the intensity of the radiation (in watts per square meter),
- \( c \) is the speed of light in vacuum (approximately \( 3 \times 10^8 \) m/s).

**Step 2: Substitute the given values into the formula.**
Given:
- Intensity \( I = 1500 \, \text{W/m}^2 \)
- Speed of light \( c = 3 \times 10^8 \, \text{m/s} \)

Now substituting these values into the formula:
\[ P = \frac{1500 \, \text{W/m}^2}{3 \times 10^8 \, \text{m/s}} \]

**Step 3: Perform the calculation.**
Calculating the above expression:
\[ P = \frac{1500}{3 \times 10^8} = \frac{1500}{300000000} = 5 \times 10^{-6} \, \text{N/m}^2 \]

**Step 4: Convert the pressure into multiples of \( 10^6 \, \text{N/m}^2 \).**
To express \( P \) in multiples of \( 10^6 \, \text{N/m}^2 \):
\[ P = 5 \times 10^{-6} \, \text{N/m}^2 = 5 \times 10^{-6} \times \frac{10^6}{10^6} = \frac{5}{10^6} \, \text{N/m}^2 \]

Thus, the radiation pressure in multiples of \( 10^6 \, \text{N/m}^2 \) is:
\[ P = 5 \times 10^{-12} \, \text{N/m}^2 \]

**Final Answer:**
The radiation pressure is \( 5 \times 10^{-12} \, \text{N/m}^2 \).

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