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. `0.332xx10^(-8)"N m"^(-2)`
C. `0.111xx10^(-8)"N m"^(-2)`
D. `0.083xx10^(-8)"N m"^(-2)`

Explanation

To find the pressure on a metal plate when radiations of intensity \(0.5 \, \text{W/m}^2\) are striking it, we can use the relationship between intensity, pressure, and the speed of light.

### Step-by-Step Solution:

1. **Understand the relationship**: The intensity \(I\) of electromagnetic radiation is related to the pressure \(P\) exerted by the radiation on a surface and the speed of light \(c\) by the formula:
\[ I = P \cdot c \]
where \(c\) is the speed of light in vacuum, approximately \(3 \times 10^8 \, \text{m/s}\).

2. **Rearrange the formula**: To find the pressure \(P\), we can rearrange the formula:
\[ P = \frac{I}{c} \]

3. **Substitute the values**: Given that the intensity \(I = 0.5 \, \text{W/m}^2\) and \(c = 3 \times 10^8 \, \text{m/s}\), we can substitute these values into the equation:
\[ P = \frac{0.5}{3 \times 10^8} \]

4. **Calculate the pressure**: Now, perform the calculation:
\[ P = \frac{0.5}{3 \times 10^8} = \frac{0.5}{300000000} \approx 1.6667 \times 10^{-9} \, \text{N/m}^2 \]

5. **Round the result**: Rounding this value gives:
\[ P \approx 1.66 \times 10^{-9} \, \text{N/m}^2 \]

### Final Answer:
The pressure on the plate is approximately \(1.66 \times 10^{-9} \, \text{N/m}^2\).

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