A radio transmitter operates at a frequency of `880 kHz` and a power of `10 kW`. The number of photons emitted per second are

Options

A. `1.72 xx 10^(31)`
B. `1327 xx 10^(34)`
C. `13.27 xx 10^(34)`
D. `0.075 xx 10^(-34)`

Explanation

To find the number of photons emitted per second by a radio transmitter operating at a frequency of 880 kHz and a power of 10 kW, we can follow these steps:

### Step 1: Understand the relationship between power, energy, and number of photons
The power (P) of the transmitter is related to the energy (E) emitted per second and the number of photons (N) emitted per second. The relationship can be expressed as:
\[ P = \frac{E}{T} = \frac{N \cdot E_{\text{photon}}}{T} \]
where \( E_{\text{photon}} \) is the energy of a single photon.

### Step 2: Calculate the energy of a single photon
The energy of a single photon can be calculated using the formula:
\[ E_{\text{photon}} = h \cdot \nu \]
where:
- \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \text{J s} \))
- \( \nu \) is the frequency of the radiation (in Hz)

Given that the frequency \( \nu = 880 \, \text{kHz} = 880 \times 10^3 \, \text{Hz} \), we can calculate the energy of a single photon.

### Step 3: Substitute the values into the energy formula
Substituting the values into the formula for energy:
\[ E_{\text{photon}} = 6.626 \times 10^{-34} \, \text{J s} \times 880 \times 10^3 \, \text{Hz} \]

### Step 4: Calculate the energy of a single photon
Now, let's calculate:
\[ E_{\text{photon}} = 6.626 \times 10^{-34} \times 880 \times 10^3 \]
\[ E_{\text{photon}} \approx 5.83 \times 10^{-28} \, \text{J} \]

### Step 5: Calculate the number of photons emitted per second
Now, we can rearrange the power equation to solve for the number of photons emitted per second:
\[ N = \frac{P}{E_{\text{photon}}} \]
Given that the power \( P = 10 \, \text{kW} = 10 \times 10^3 \, \text{W} \):
\[ N = \frac{10 \times 10^3}{5.83 \times 10^{-28}} \]

### Step 6: Perform the calculation
Calculating the number of photons:
\[ N \approx \frac{10^4}{5.83 \times 10^{-28}} \]
\[ N \approx 1.71 \times 10^{31} \]

### Final Answer
The number of photons emitted per second is approximately:
\[ N \approx 1.71 \times 10^{31} \]