Estimate the following the following two numbers should be interesting. The first number will tell you why radio engineers do not need to worry much about a photons. The second number tells you why our eye can never "count photon" even in barely detectable light.
(i) The number of photons emitted per second by a MW transmitter of 10kW power emitting radiowaves of length 500m.
(ii) The number of photons entering the pupil of our eye per second corresponding to the minimum intensity of white light that we humans can perceive `(~10^(-10)Wm^(-2))`. Take the area of the pupil to be about `0.4cm^(2)`, and the average frequency of white light to be about `6xx10^(4)Hz. (h=6.6xx10^(-34)J)`

Explanation

(a) For `lambda=500m, E=(hc//lambda)=3.98xx10^(-28)J`. Number of photons emitted per second
`=10^(4)Js^(-1)//3.98xx10^(-28)J~=3xx10^(31)s^(-1)`
We see that the energy of a radiophoton is exceedingly small, and the number of photons emitted per second in a radio beam is enormously large. There is, therefore, negligible error involved in ignoring the existence of a minimum quantum of energy (photon) and treating the total energy of a radio wave as continuous.
For `ν = 6 xx10^(14) Hz, E ~ 4 xx 10^(-19)J`. Photon flux corresponding to minimum intensity
`= 10^(-10) W m^(-2)//4xx10^(-19)J = 2.5 xx 10^(8) m^(-2) s^(-1)`
Number of photons entering the pupil per second `=2.5xx10^(8)xx0.4xx10^(-4)s^(-1)=10^(4)s^(-1)`. Though this number is not as large as in (a) above, it is large enough for us never to ‘sense’ or ‘count’ individual photons by our eye.