A radio station is transmitting waves of wavelength 300 m. Radiation capacity of the transmitter is 10 kW, The number of photons emitted per unit time is

Options

A. `1.5xx10^(35)`
B. `1.5xx10^(29)`
C. `1.5xx10^(33)`
D. `1.5xx10^(31)`

Explanation

To solve the problem of finding the number of photons emitted per unit time by a radio station transmitting waves of wavelength 300 m with a radiation capacity of 10 kW, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values**:
- Wavelength (λ) = 300 m
- Power (P) = 10 kW = 10 × 10^3 W
- Planck's constant (h) = 6.63 × 10^(-34) J·s
- Speed of light (c) = 3 × 10^8 m/s

2. **Calculate Frequency (ν)**:
The frequency of the wave can be calculated using the formula:
\[ \nu = \frac{c}{\lambda} \]
Substituting the values:
\[ \nu = \frac{3 \times 10^8 \text{ m/s}}{300 \text{ m}} = 1 \times 10^6 \text{ Hz} \]

3. **Calculate Energy of a Single Photon (E)**:
The energy of a single photon can be calculated using Planck's equation:
\[ E = h \nu \]
Substituting the values:
\[ E = (6.63 \times 10^{-34} \text{ J·s}) \times (1 \times 10^6 \text{ Hz}) = 6.63 \times 10^{-28} \text{ J} \]

4. **Calculate Number of Photons Emitted per Unit Time (n)**:
The number of photons emitted per unit time can be calculated using the formula:
\[ n = \frac{P}{E} \]
Substituting the values:
\[ n = \frac{10 \times 10^3 \text{ W}}{6.63 \times 10^{-28} \text{ J}} \approx 1.51 \times 10^{31} \text{ photons/s} \]

5. **Final Result**:
The number of photons emitted per unit time is approximately:
\[ n \approx 1.5 \times 10^{31} \text{ photons/s} \]