A monochromatic source emits light of wavelength 550 nm is emitted by a source . Find the number of photons emitted by the source in 90 seconds if power of source is 60 W.

Answer

To solve the problem of finding the number of photons emitted by a monochromatic light source in a given time, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values:**
- Wavelength of light, \( \lambda = 550 \, \text{nm} = 550 \times 10^{-9} \, \text{m} \)
- Power of the source, \( P = 60 \, \text{W} \)
- Time, \( t = 90 \, \text{s} \)

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

Substituting the values:
\[ E = \frac{(6.626 \times 10^{-34} \, \text{J s})(3 \times 10^8 \, \text{m/s})}{550 \times 10^{-9} \, \text{m}} \]

3. **Calculate the Total Energy Emitted in 90 Seconds:**
The total energy \( E_{total} \) emitted by the source in 90 seconds can be calculated using:
\[ E_{total} = P \times t \]
Substituting the values:
\[ E_{total} = 60 \, \text{W} \times 90 \, \text{s} = 5400 \, \text{J} \]

4. **Calculate the Number of Photons Emitted:**
The number of photons \( n \) emitted can be calculated using the formula:
\[ n = \frac{E_{total}}{E} \]
Substituting the values:
\[ n = \frac{5400 \, \text{J}}{E} \]

5. **Final Calculation:**
After calculating \( E \) from step 2, substitute it back into the equation for \( n \) to find the total number of photons emitted in 90 seconds.