Radiations of intensity `0.5 W//m^(2)` are striking a metal plate. The pressure on the plate is

Options

A. `0.166xx10^(-8)N//m^(2)`
B. `0.33xx10^(-8)N//m^(2)`
C. `0.111xx10^(-8)N//m^(2)`
D. `0.083xx10^(-8)N//m^(2)`

Explanation

To find the pressure exerted on a metal plate by radiation of intensity \( I = 0.5 \, \text{W/m}^2 \), we can use the formula for radiation pressure.

### Step-by-Step Solution:

1. **Understand the Concept of Radiation Pressure**:
Radiation pressure is the pressure exerted by electromagnetic radiation on a surface. It can be calculated using the formula:
\[ P = \frac{I}{c} \]
where \( P \) is the radiation pressure, \( I \) is the intensity of the radiation, and \( c \) is the speed of light in vacuum.

2. **Identify the Values**:
- Given intensity \( I = 0.5 \, \text{W/m}^2 \)
- The speed of light \( c \approx 3 \times 10^8 \, \text{m/s} \)

3. **Substitute the Values into the Formula**:
\[ P = \frac{0.5 \, \text{W/m}^2}{3 \times 10^8 \, \text{m/s}} \]

4. **Calculate the Pressure**:
\[ P = \frac{0.5}{3 \times 10^8} = \frac{0.5}{3} \times 10^{-8} = \frac{1}{6} \times 10^{-8} \approx 0.1667 \times 10^{-8} \, \text{N/m}^2 \]
Thus, the pressure on the plate is approximately:
\[ P \approx 1.67 \times 10^{-9} \, \text{N/m}^2 \]

### Final Answer:
The pressure on the plate is approximately \( 1.67 \times 10^{-9} \, \text{N/m}^2 \).