Electromagnetic radiation with energy flux `50W cm^(-2)` is incident on a totally absorbing surface normally for `1 hour`: If the surface has an area of `0.05m^(2)`, then the avergae force due to the radiaton pressure, on it is,

Options

A. `8.3xx10^(-7)N`
B. `8.3xx10^(-5)N`
C. `1.2xx10^(-7)N`
D. `1.2xx10^(-5)N`

Explanation

To find the average force due to the radiation pressure on a totally absorbing surface, we can follow these steps:

### Step 1: Understand the given data
- Energy flux (I) = 50 W/cm²
- Area (A) = 0.05 m²
- Time (t) = 1 hour = 3600 seconds

### Step 2: Convert energy flux to SI units
Energy flux is given in W/cm². We need to convert it to W/m²:
\[ 1 \text{ cm}^2 = 10^{-4} \text{ m}^2 \]
Thus,
\[ I = 50 \text{ W/cm}^2 = 50 \times 10^4 \text{ W/m}^2 = 5 \times 10^6 \text{ W/m}^2 \]

### Step 3: Calculate the total power incident on the surface
The total power (P) incident on the surface can be calculated using:
\[ P = I \times A \]
Substituting the values:
\[ P = 5 \times 10^6 \text{ W/m}^2 \times 0.05 \text{ m}^2 = 250000 \text{ W} \]

### Step 4: Calculate the radiation pressure
For a totally absorbing surface, the radiation pressure (P_r) can be calculated using the formula:
\[ P_r = \frac{I}{c} \]
Where \( c \) is the speed of light, approximately \( 3 \times 10^8 \text{ m/s} \).

### Step 5: Calculate the average force
The average force (F) on the surface due to radiation pressure can be calculated using:
\[ F = P_r \times A \]
Substituting the values:
\[ F = \frac{I}{c} \times A \]
\[ F = \frac{5 \times 10^6 \text{ W/m}^2}{3 \times 10^8 \text{ m/s}} \times 0.05 \text{ m}^2 \]
Calculating this gives:
\[ F = \frac{5 \times 10^6 \times 0.05}{3 \times 10^8} \]
\[ F = \frac{250000}{3 \times 10^8} \]
\[ F \approx 8.33 \times 10^{-5} \text{ N} \]

### Final Answer
The average force due to the radiation pressure on the surface is approximately \( 8.33 \times 10^{-5} \text{ N} \).

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