Question

An FM radio transmitter broadcasts at 98.4 MHz with a power of

45 kW. How many photons does it generate per second?

Answer 1

6.9 × 10²⁹ photons

Step-by-step explanation:

Given:

Frequency, υ = 98.4 MHz = 98.4 × 10⁶ Hz

Power, P = 45 kW = 45000 J/sec

Now,

The total energy in time, t = 1 second

E = P × t = 45000 J/sec × 1 s

or

Energy = 45000 J

also,

Energy of photons = hυ

Where, h is the Plank's constant

or

Energy of photons = 6.625 × 10⁻³⁴ × 98.4 × 10⁶

or

Energy of photons = 6.519 × 10⁻²⁶ J

Now,

number of photons =
`\frac{\textup{Total Energy}}{\textup{Energy of Photon}}`

or

n =
`(45000)/(6.519*10^(-26))`

or

n = 6.9 × 10²⁹ photons