Question

A $\mathbf{940}\mathbf{}\mathit{k}\mathit{H}\mathit{z}$ radio station broadcasts of power. How many photons emanate from the transmitting antenna every second?

Short answer

The number of photons is $6.4\times {10}^{31}$, emanate from the transmitting antenna every second.

Step-by-step solution

Step 1:

In specifically, a photon's energy is equal to the radiation frequency multiplied by Planck's

constant.

The radio station produces many photons, each having an energy of $hf$. The radio station emits $n$number of photons. The station's energy output, therefore, becomes $n$times the energy of each photon:

$E=nhf$

Here, is the energy of a photon, is the number of photons, is the plank’s constant, and is the frequency.

That energy is then employed in the power equation as follows:

localid="1657554687931" $$\begin{gathered} P=\frac{E}{t} \\ =\frac{nhf}{t} \end{gathered}$$

Rearrange the above equation for the number of photons.

$n=\frac{Pt}{hf}$ ….. (1)

Consider the known data as below.

The power, $P=40kW=40000W$

The frequency, $f=940kHz=940000Hz$

Plank’s constant, localid="1657554880833" $h=6.636\times {10}^{-34}J\cdot s$

Speed of light, $c=3\times {10}^8\frac{m}{s}$

Substitute known values into equation (1), and you have

localid="1657555089397" $$\begin{gathered} \mathrm{n}=\frac{40000\times 1}{6.636\times {10}^{-34}\times 940000} \\ 6.4\times {10}^{-34} \end{gathered}$$

Hence, the number of photons emitted every second is $6.4\times {10}^{-34}$.