A 100 W point source emits monochromatic light of wavelength `6000 A`
Calculate the total number of photons emitted by the source per second.

Options

A. `5xx10^(20)`
B. `8xx10^(20)`
C. `6xx10^(21)`
D. `3xx10^(20)`

Explanation

To solve the problem of calculating the total number of photons emitted by a 100 W point source of monochromatic light with a wavelength of 6000 Å, we can follow these steps:

### Step 1: Understand the Energy of a Photon
The energy \( E \) of a single photon can be calculated using the formula:
\[ E = \frac{hc}{\lambda} \]
where:
- \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \text{J s} \)),
- \( c \) is the speed of light (\( 3 \times 10^8 \, \text{m/s} \)),
- \( \lambda \) is the wavelength of light.

### Step 2: Convert Wavelength to Meters
The wavelength is given in angstroms (Å). We need to convert it to meters:
\[ \lambda = 6000 \, \text{Å} = 6000 \times 10^{-10} \, \text{m} = 6 \times 10^{-7} \, \text{m} \]

### Step 3: Calculate the Energy of One Photon
Substituting the values into the energy formula:
\[ E = \frac{(6.626 \times 10^{-34} \, \text{J s})(3 \times 10^8 \, \text{m/s})}{6 \times 10^{-7} \, \text{m}} \]
Calculating this gives:
\[ E = \frac{1.9878 \times 10^{-25} \, \text{J m}}{6 \times 10^{-7} \, \text{m}} = 3.313 \times 10^{-19} \, \text{J} \]

### Step 4: Relate Power to Energy and Number of Photons
Power is defined as energy per unit time:
\[ P = \frac{E_{\text{total}}}{t} \]
where \( E_{\text{total}} \) is the total energy emitted in time \( t \). For one second, we have:
\[ E_{\text{total}} = P \times t = 100 \, \text{W} \times 1 \, \text{s} = 100 \, \text{J} \]

### Step 5: Calculate the Number of Photons Emitted Per Second
The total energy emitted can also be expressed in terms of the number of photons \( n \) and the energy of one photon \( E \):
\[ E_{\text{total}} = n \times E \]
Thus, we can rearrange this to find \( n \):
\[ n = \frac{E_{\text{total}}}{E} = \frac{100 \, \text{J}}{3.313 \times 10^{-19} \, \text{J}} \]
Calculating this gives:
\[ n \approx 3.01 \times 10^{20} \, \text{photons} \]

### Final Answer
The total number of photons emitted by the source per second is approximately:
\[ n \approx 3 \times 10^{20} \, \text{photons per second} \]

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