Question

A radio transmitter operates at a frequency of 880 kHz and power of 10 kW. The number of photons emitted per second is:
A. $13.27\times 10^4$
B. $13.27\times 10^{34}$
C. $1327\times 10^{34}$
D. $1.71\times 10^{31}$

Answer 1

Hint: The photons emitted will have some energy of their own and the power of the radio wave coming from the transmitter will be determined by the number of photons emitted per second. So, we will first find the energy of each photon and then equate it with the power given, we will get the number of photons emitted.

Formula used:
Power, $P=nhv$

Complete step by step solution:
We have been given the power of a radio transmitter, $P=10kW$ and its frequency is $v=880kHz$.
Since, energy of a photon having frequency $v$ is given by $E=hv$, where h is the Planck’s constant having value $6.63\times 10^{-34}J-s$.
Therefore, energy of $n$ photons will be $E=nhv$
And so, the power will be the energy per second and as the time is one second, the power can be given by
$P=nhv\implies n=\dfrac{P}{hv}=\dfrac{10000}{6.63\times 10^{-34} \times 880000}=1.71\times 10^{31}$
Hence, option d is the correct answer.

Additional information:
Radio transmitters are used in devices that communicate with radio such as the radios we used to have in our homes, the television broadcasts, satellite communications, etc. The information from such types of devices are carried by radio waves which are emitted by a transmitter and is received by a receiver. In radars, which are used to track and locate different objects like missiles, spacecraft etc. radio waves are used and thus all these devices require radio transmitters.

Note: Power is given by the work done per unit time or the change in energy per unit time and here the energy is released in the form of photons and we have calculated that for one second.