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.

Step-by-step explanation:

Power and energy are related as

`P=(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}*10^(-34)\text{ J s}`

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

`\begin{gathered} P=\text{ nhf} \\ n=(P)/(hf) \\ =\frac{35*10^3W}{6.6*10^(-34)\text{ J.s }*2766*10^3\text{ Hz}} \\ =1.92*10^(31)\text{ photons each second} \end{gathered}`

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