About `6%` of the power of a 100 W light bulb is converted to visible radiation. The average intensity of visible radiation at a distance of 8 m is (Assume that the radiation is emitted isotropically and neglect reflection.)

Options

A. `3.5xx10^(-3)"W m"^(-2)`
B. `5.1xx10^(-3)"W m"^(-2)`
C. `7.2xx10^(-3)"W m"^(-2)`
D. `2.3xx10^(-3)"W m"^(-2)`

Explanation

To solve the problem step by step, we will calculate the average intensity of visible radiation emitted by a 100 W light bulb at a distance of 8 m, given that 6% of the power is converted to visible radiation.

### Step 1: Calculate the Effective Power of Visible Radiation
The total power of the light bulb is 100 W, and only 6% of this power is converted to visible radiation.

\[ \text{Effective Power} = 6\% \text{ of } 100 \text{ W} = \frac{6}{100} \times 100 = 6 \text{ W} \]

### Step 2: Calculate the Area of the Sphere at 8 m
Since the radiation is emitted isotropically, we can consider the light spreading out uniformly in all directions, forming a sphere. The formula for the surface area \(A\) of a sphere is given by:

\[ A = 4 \pi r^2 \]

Where \(r\) is the radius (distance from the bulb). Here, \(r = 8 \text{ m}\).

\[ A = 4 \pi (8)^2 = 4 \pi (64) = 256 \pi \text{ m}^2 \]

### Step 3: Calculate the Intensity of Visible Radiation
Intensity \(I\) is defined as the power per unit area. Therefore, we can calculate the intensity of the visible radiation using the effective power and the area we just calculated.

\[ I = \frac{\text{Power}}{\text{Area}} = \frac{6 \text{ W}}{256 \pi \text{ m}^2} \]

### Step 4: Simplify the Expression
Now, we can calculate the numerical value of the intensity.

\[ I = \frac{6}{256 \pi} \approx \frac{6}{804.25} \approx 0.00748 \text{ W/m}^2 \]

### Step 5: Express in Scientific Notation
To express the intensity in scientific notation:

\[ I \approx 7.48 \times 10^{-3} \text{ W/m}^2 \]

### Final Answer
The average intensity of visible radiation at a distance of 8 m is approximately:

\[ I \approx 7.48 \times 10^{-3} \text{ W/m}^2 \]

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