A 100 W point source emits monochromatic light of wavelength `6000 A`
Q. Calculate the photon flux (in SI unit) at a distance of 5m from the source. Given `h=6.6xx10^(34)`J s and `c=3xx10^(8)ms^(-1)`

Options

A. `10^(15)`
B. `10^(18)`
C. `10^(20)`
D. `10^(22)`

Explanation

To solve the problem of calculating the photon flux at a distance of 5m from a 100 W point source emitting monochromatic light of wavelength 6000 Å, we will follow these steps:

### Step 1: Convert Wavelength to Meters
The wavelength is given as 6000 Å (angstroms). We need to convert this to meters.

\[ \text{Wavelength} (\lambda) = 6000 \, \text{Å} = 6000 \times 10^{-10} \, \text{m} = 6.0 \times 10^{-7} \, \text{m} \]

### Step 2: Calculate the Energy of One Photon
The energy of a single photon can be calculated using the formula:

\[ E = \frac{hc}{\lambda} \]

Where:
- \( h = 6.6 \times 10^{-34} \, \text{J s} \) (Planck's constant)
- \( c = 3 \times 10^{8} \, \text{m/s} \) (speed of light)

Substituting the values:

\[ E = \frac{(6.6 \times 10^{-34} \, \text{J s}) \times (3 \times 10^{8} \, \text{m/s})}{6.0 \times 10^{-7} \, \text{m}} \]

Calculating this gives:

\[ E = \frac{1.98 \times 10^{-25} \, \text{J m}}{6.0 \times 10^{-7} \, \text{m}} = 3.30 \times 10^{-19} \, \text{J} \]

### Step 3: Calculate the Number of Photons Emitted per Second
The power of the source is given as 100 W, which is equivalent to 100 J/s. The number of photons emitted per second (\( n \)) can be calculated using:

\[ n = \frac{P}{E} \]

Where \( P = 100 \, \text{W} \) and \( E \) is the energy of one photon calculated in the previous step.

Substituting the values:

\[ n = \frac{100 \, \text{J/s}}{3.30 \times 10^{-19} \, \text{J}} \approx 3.03 \times 10^{20} \, \text{photons/s} \]

### Step 4: Calculate the Area at a Distance of 5m
The photons emitted from the point source spread out uniformly in all directions, forming a sphere. The area of a sphere is given by:

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

Where \( r = 5 \, \text{m} \).

Calculating the area:

\[ A = 4 \pi (5^2) = 4 \pi (25) = 100 \pi \approx 314 \, \text{m}^2 \]

### Step 5: Calculate the Photon Flux
Photon flux (\( \Phi \)) is defined as the number of photons striking a unit area per second. It can be calculated using:

\[ \Phi = \frac{n}{A} \]

Substituting the values we have:

\[ \Phi = \frac{3.03 \times 10^{20} \, \text{photons/s}}{314 \, \text{m}^2} \approx 9.67 \times 10^{17} \, \text{photons/m}^2/\text{s} \]

### Conclusion
Thus, the photon flux at a distance of 5m from the source is approximately:

\[ \Phi \approx 9.67 \times 10^{17} \, \text{photons/m}^2/\text{s} \approx 10^{18} \, \text{photons/m}^2/\text{s} \]