An AIR station is broadcasting the waves of wavelength `300 metres`. If the radiating power of the transmitter is `10 kW`, then the number of photons radiated per second is

Explanation

To solve the problem of finding the number of photons radiated per second by an AIR station broadcasting waves of wavelength 300 meters with a radiating power of 10 kW, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values**:
- Wavelength (\( \lambda \)) = 300 meters
- Power of the transmitter (\( P \)) = 10 kW = 10,000 W

2. **Calculate the energy of a single photon**:
The energy of a photon can be calculated using the formula:
\[ E = \frac{hc}{\lambda} \]
where:
- \( h \) (Planck's constant) = \( 6.626 \times 10^{-34} \, \text{Js} \)
- \( c \) (speed of light) = \( 3 \times 10^8 \, \text{m/s} \)
- \( \lambda \) = 300 m

Plugging in the values:
\[ E = \frac{(6.626 \times 10^{-34} \, \text{Js}) \times (3 \times 10^8 \, \text{m/s})}{300 \, \text{m}} \]
\[ E = \frac{1.9878 \times 10^{-25} \, \text{J}}{300} \]
\[ E = 6.626 \times 10^{-28} \, \text{J} \]

3. **Calculate the total energy radiated per second**:
Since the power is given in watts (joules per second), the total energy radiated per second is:
\[ E_{\text{total}} = 10,000 \, \text{J/s} \]

4. **Calculate the number of photons emitted per second**:
The number of photons (\( n \)) emitted per second can be calculated using the formula:
\[ n = \frac{E_{\text{total}}}{E} \]
Substituting the values:
\[ n = \frac{10,000 \, \text{J/s}}{6.626 \times 10^{-28} \, \text{J}} \]
\[ n \approx 1.51 \times 10^{31} \, \text{photons/s} \]

### Final Answer:
The number of photons radiated per second is approximately \( 1.51 \times 10^{31} \) photons/s.

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