The incident intensity on a horizontal surface at sea level from the sun is about `1kW m^(-2)`.
Q. Find the ratio of this pressure to atmospheric pressure `p_0` (about `1xx10^(5)` Pa) at sea level

Options

A. `5xx10^(-11)`
B. `4xx10^(-8)`
C. `6xx10^(-12)`
D. `8xx10^(-11)`

Explanation

To solve the problem, we need to find the ratio of the radiation pressure exerted by sunlight on a surface to the atmospheric pressure at sea level. Here’s a step-by-step solution:

### Step 1: Understanding the Intensity of Light
The intensity \( S \) of sunlight incident on a horizontal surface is given as \( 1 \, \text{kW/m}^2 \). We need to convert this into standard SI units:
\[ S = 1 \, \text{kW/m}^2 = 1000 \, \text{W/m}^2 \]

### Step 2: Calculating Radiation Pressure
The pressure \( P \) exerted by the absorbed light can be calculated using the formula:
\[ P = \frac{1}{2} \frac{S}{c} \]
where \( c \) is the speed of light, approximately \( 3 \times 10^8 \, \text{m/s} \).

Substituting the values:
\[ P = \frac{1}{2} \frac{1000}{3 \times 10^8} \]
Calculating this gives:
\[ P = \frac{1000}{2 \times 3 \times 10^8} = \frac{1000}{6 \times 10^8} = \frac{1}{6 \times 10^5} \approx 1.67 \times 10^{-6} \, \text{Pa} \]

### Step 3: Considering Reflected Light
The pressure exerted by reflected light is given by:
\[ P_{\text{reflected}} = \frac{2S}{3c} \]
Substituting the values:
\[ P_{\text{reflected}} = \frac{2 \times 1000}{3 \times 3 \times 10^8} = \frac{2000}{9 \times 10^8} \approx 2.22 \times 10^{-6} \, \text{Pa} \]

### Step 4: Total Radiation Pressure
The total radiation pressure \( P_{\text{total}} \) on the surface is the sum of the pressures from absorbed and reflected light:
\[ P_{\text{total}} = P + P_{\text{reflected}} = 1.67 \times 10^{-6} + 2.22 \times 10^{-6} = 3.89 \times 10^{-6} \, \text{Pa} \]

### Step 5: Atmospheric Pressure
The atmospheric pressure \( P_0 \) at sea level is given as:
\[ P_0 = 1 \times 10^5 \, \text{Pa} \]

### Step 6: Finding the Ratio
Now, we can find the ratio of the radiation pressure to the atmospheric pressure:
\[ \text{Ratio} = \frac{P_{\text{total}}}{P_0} = \frac{3.89 \times 10^{-6}}{1 \times 10^5} \]
Calculating this gives:
\[ \text{Ratio} = 3.89 \times 10^{-11} \]

### Final Answer
Thus, the ratio of the radiation pressure to atmospheric pressure is:
\[ \text{Ratio} \approx 3.89 \times 10^{-11} \]