Question

A 2,766 kHz AM radio station broadcasts with a power of 35 kW. How many photons does the transmitting antenna emit each second?

Answer 1

Given:

The frequency of the wave is f = 2766 kHz

The power is P = 35 kW

Required: Number of photons emit each second by the transmitting antenna.

Explanation:

Power and energy are related as

$P=\frac{E}{t}$

For each second the time will be t = 1 s

Also, the energy can be calculated by the formula

$E=nhf$

Here, Planck's constant is

$h\text{ = 6.6}\times10^{-34}\text{ J s}$

On substituting the values, the number of photons each second will be

$\begin{gathered} P=\text{ nhf} \\ n=\frac{P}{hf} \\ =\frac{35\times10^3W}{6.6\times10^{-34}\text{ J.s }\times2766\times10^3\text{ Hz}} \\ =1.92\times10^{31}\text{ photons each second} \end{gathered}$

Final Answer: There are 1.92 x 10^(31) photons each second.