The number of photons per second on an average emitted by the source of monochromatic light of wavelength 600nm , when it delivers the power of `3.3 xx 10^(-3)` watt will be `(h = 6.6 xx10^(-34) Js)`

Options

A. `10^(17)`
B. `10^(16)`
C. `10^(15)`
D. `10^(18)`

Explanation

To find the number of photons emitted per second by a source of monochromatic light, we can use the relationship between power, energy, and the energy of a single photon.

### Step-by-Step Solution:

1. **Understand the relationship between power, energy, and time**:
Power (P) is defined as energy (E) per unit time (t). For our case, we can express this as:
\[ P = \frac{E}{t} \]
Since we are interested in the number of photons emitted per second, we can set \( t = 1 \) second. Thus, the power is equal to the energy emitted in one second.

2. **Calculate the energy of a single photon**:
The energy of a single photon can be calculated using the formula:
\[ E = \frac{hc}{\lambda} \]
where:
- \( h \) is Planck's constant (\( 6.6 \times 10^{-34} \, \text{Js} \)),
- \( c \) is the speed of light (\( 3 \times 10^{8} \, \text{m/s} \)),
- \( \lambda \) is the wavelength of the light.

Given \( \lambda = 600 \, \text{nm} = 600 \times 10^{-9} \, \text{m} \).

3. **Substitute the values into the energy formula**:
\[ E = \frac{(6.6 \times 10^{-34} \, \text{Js})(3 \times 10^{8} \, \text{m/s})}{600 \times 10^{-9} \, \text{m}} \]

4. **Calculate the energy of a single photon**:
\[ E = \frac{(6.6 \times 3) \times 10^{-34 + 8 + 9}}{600} \]
\[ E = \frac{19.8 \times 10^{-17}}{600} \]
\[ E = 3.3 \times 10^{-19} \, \text{J} \]

5. **Calculate the number of photons emitted per second**:
The number of photons emitted per second (\( n \)) can be calculated using the formula:
\[ n = \frac{P}{E} \]
Given \( P = 3.3 \times 10^{-3} \, \text{W} \):
\[ n = \frac{3.3 \times 10^{-3}}{3.3 \times 10^{-19}} \]
\[ n = 10^{16} \]

### Final Answer:
The number of photons emitted per second is approximately \( 10^{16} \).