Question

Your favorite radio station broadcasts at a frequency of 83.8 MHz with a power of 32.5 kW. How many photons does the antenna of the station emit in each second?

Answer 1

The antenna emits
`5.85* 10^(19)` photons per second.

Step-by-step explanation:

Given:

Power of the antenna is,
`P=32.5\ kW=32.5* 10^3\ W`

Frequency of the antenna is,
`f=83.8\ MHz=83.8* 10^6\ Hz`

Now, energy possessed by 1 photon is given as:

`E=h\cdot f\\Where,h\to \textrm{Planck's constant}`

Here,
`f=83.8* 10^6\ Hz,h=6.626* 10^(-34)\ J.s`. So,

`E=(6.626* 10^(-34)\ J.s)(83.8* 10^6\ Hz)=5.5526* 10^(-26)\ J`

Also, total energy of the antenna per second is equal to its power which is equal to
`32.5* 10^3` J.

Now, number of photons emitted each second is given as:

`n=\frac{\textrm{Total energy of the antenna per second}}{\textrm{Energy of 1 photon}}\\n=(32.5* 10^3\ J/s)/(5.5526* 10^(-26)\ J)\\n=5.85* 10^(19)\textrm{ photons per sec}`

Therefore, the antenna emits
`5.85* 10^(19)` photons per second.