A monochromatic source of light emits photons of frequency `6 xx 10^(14 )Hz` . The power emitted by the source is 8 x 10^(-3)W. Calculate the number of photons emitted per second. (Take ` h = 6.63 xx 10^(-34) Js`)

Options

A. `6 xx 10^(14)`
B. `4 xx 10^(15)`
C. `2 xx 10^(16)`
D. `1 xx 10^(17)`

Explanation

To solve the problem of calculating the number of photons emitted per second by a monochromatic light source, we can follow these steps:

### Step 1: Understand the given data
- Frequency of the emitted photons, \( \nu = 6 \times 10^{14} \, \text{Hz} \)
- Power emitted by the source, \( P = 8 \times 10^{-3} \, \text{W} \)
- Planck's constant, \( h = 6.63 \times 10^{-34} \, \text{Js} \)

### Step 2: Calculate the energy of one photon
The energy \( E \) of a single photon can be calculated using the formula:
\[ E = h \nu \]
Substituting the given values:
\[ E = (6.63 \times 10^{-34} \, \text{Js}) \times (6 \times 10^{14} \, \text{Hz}) \]

### Step 3: Perform the multiplication
Calculating the energy:
\[ E = 6.63 \times 6 \times 10^{-34} \times 10^{14} = 39.78 \times 10^{-20} \, \text{J} \]
This can be approximated as:
\[ E \approx 3.978 \times 10^{-19} \, \text{J} \]

### Step 4: Calculate the number of photons emitted per second
The number of photons emitted per second \( n \) can be found using the formula:
\[ n = \frac{P}{E} \]
Substituting the values:
\[ n = \frac{8 \times 10^{-3} \, \text{W}}{3.978 \times 10^{-19} \, \text{J}} \]

### Step 5: Perform the division
Calculating the number of photons:
\[ n \approx \frac{8 \times 10^{-3}}{3.978 \times 10^{-19}} \approx 2.01 \times 10^{16} \, \text{photons/s} \]

### Final Answer
The number of photons emitted per second is approximately:
\[ n \approx 2 \times 10^{16} \, \text{photons/s} \]

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