Radiation of intensity `1 W//m^(2)` are striking on a metal plate. The pressure on the plate is

Options

A. `0.66 xx 10^(-8) N//m^(2)`
B. `0.25 N//m^(2)`
C. `2 N//m^(2)`
D. `4 N//m^(2)`

Explanation

To find the pressure on a metal plate due to radiation of intensity \(1 \, \text{W/m}^2\), we can use the relationship between intensity and pressure. The formula for the pressure \(P\) exerted by radiation is given by:

\[ P = \frac{2I}{c} \]

where:
- \(I\) is the intensity of the radiation,
- \(c\) is the speed of light in vacuum, approximately \(3 \times 10^8 \, \text{m/s}\).

### Step-by-Step Solution:

1. **Identify the given values:**
- Intensity \(I = 1 \, \text{W/m}^2\)
- Speed of light \(c = 3 \times 10^8 \, \text{m/s}\)

2. **Substitute the values into the formula:**
\[ P = \frac{2 \times 1 \, \text{W/m}^2}{3 \times 10^8 \, \text{m/s}} \]

3. **Calculate the numerator:**
\[ 2 \times 1 = 2 \, \text{W/m}^2 \]

4. **Now divide by the speed of light:**
\[ P = \frac{2}{3 \times 10^8} \]

5. **Perform the division:**
\[ P = \frac{2}{3} \times 10^{-8} \, \text{N/m}^2 \]

6. **Calculate \(\frac{2}{3}\):**
\[ \frac{2}{3} \approx 0.6667 \]

7. **Final result:**
\[ P \approx 0.6667 \times 10^{-8} \, \text{N/m}^2 \approx 0.67 \times 10^{-8} \, \text{N/m}^2 \]

Thus, the pressure on the plate is approximately \(0.67 \times 10^{-8} \, \text{N/m}^2\).

### Final Answer:
The pressure on the plate is \(0.67 \times 10^{-8} \, \text{N/m}^2\).

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