A monochromatic light of frequency `3xx10^(14)Hz` is produced by a LASER, emits the power of `3xx10^(-3)` W. Find how many number of photons are emitted per second.

Options

A. `1.5xx10^(16)`
B. `2.5xx10^(16)`
C. `4.5xx10^(16)`
D. `8.5xx10^(16)`

Explanation

To find the number of photons emitted per second by a laser with a given frequency and power, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Frequency of light, \( \nu = 3 \times 10^{14} \, \text{Hz} \)
- Power emitted by the laser, \( P = 3 \times 10^{-3} \, \text{W} \)

2. **Understand the Relationship Between Power, Number of Photons, and Energy of Each Photon:**
- The power emitted by the laser can be expressed as:
\[ P = n \cdot E \]
where \( n \) is the number of photons emitted per second, and \( E \) is the energy of each photon.

3. **Calculate the Energy of Each Photon:**
- The energy of a photon can be calculated using the formula:
\[ E = h \cdot \nu \]
where \( h \) is Planck's constant, approximately \( 6.626 \times 10^{-34} \, \text{J s} \).

4. **Substitute the Values to Find the Energy:**
- Substitute \( h \) and \( \nu \) into the equation:
\[ E = (6.626 \times 10^{-34} \, \text{J s}) \cdot (3 \times 10^{14} \, \text{Hz}) \]
- Calculate \( E \):
\[ E = 1.9878 \times 10^{-19} \, \text{J} \]

5. **Rearrange the Power Equation to Solve for \( n \):**
- From the power equation, we can express \( n \) as:
\[ n = \frac{P}{E} \]

6. **Substitute the Values to Find \( n \):**
- Substitute \( P \) and \( E \):
\[ n = \frac{3 \times 10^{-3} \, \text{W}}{1.9878 \times 10^{-19} \, \text{J}} \]

7. **Calculate \( n \):**
- Performing the division:
\[ n \approx 1.51 \times 10^{16} \, \text{photons per second} \]

8. **Final Result:**
- The number of photons emitted per second is approximately:
\[ n \approx 1.5 \times 10^{16} \, \text{photons per second} \]