Question

A radio transmitter is working at frequency 880 kHz and power 10kW. The number of photons emitted per second will be

• A. $1327\times {10}^{34}$
• B. $0.075\times {10}^{-34}$
• C. $1.71\times {10}^{31}$
• D. $13.27\times {10}^{34}$

Answer 1

The correct option is C $1.71\times {10}^{31}$

The energy of photon is given by
$E=h\nu$
where h is Plank's constant, $h=6.6\times {10}^{-34}Js$ and $\nu$ is the frequency of the photon.
$E=6.6\times {10}^{-34}\times 880\times {10}^3$
$E=5808\times {10}^{-31}$
$E=5.808\times {10}^{-28}J$
Now, for the n number of photons emitted per second we can write
$nE=P$ ................................(since, power is energy (emitted or absorbed) per second)

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

$n=\frac{10\times {10}^3}{5.808\times {10}^{-28}}$

$n=1.721\times {10}^{31}$

So, the answer is option (C).