Question

A TV station is operated at $100MW$ with a signal frequency of $10MHz$. Calculate the number of photons radiated per second by its antenna.

Answer 1

In the question, we are given a TV station with certain power and frequency. We need to find the number of photons present per second in the antenna. For that we had used the formula of energy of photons. Assuming the energy which is represented as the power into time. And keep in mind about the dimensions of the respective symbols.

Complete step by step answer:
Writing the formula of power, $P = nhv$ where $P$is the power per unit time, $n$is the number of photons, $h$ is planck's constant whose value is $6.64 \times {10^{ - 34}}$ $J$ and $v$ is the frequency
Values given in the question are $P = 100MH$ $v = 10MHz$
Using the formula of power to find the number of photons. $n = \dfrac{P}{{hv}}$
Substituting the values,
$n = \dfrac{{100}}{{6.64 \times {{10}^{ - 34}} \times 10}} \\\ \therefore n = 1.5 \times {10^{34}}$
Whereas energy of photons is represented as $E = nhv$.

Hence, the number of photons emitting per second $1.5 \times {10^{34}}$ photons.

Note: The units should be taken care of. The values used in the question such as $MHz$ represents megahertz whose value is ${10^6}$ Hz and is the same as with the power.Photons are referred to as the quantum of electromagnetic energy.