If an FM radio receiver can register a signal with a minimum received power of 1

Question

If an FM radio receiver can register a signal with a minimum received power of 10_12: W, how many photons per second must be collected by the receiver to detect the signal? Use 100 MHz as the frequency of the radio photons. The human eye at its limit can detect light an intensity of 10 12-W m. under optimal conditions. How many photons with X = 550 nm must be collected in 1/30 of a second (which is how long a neuron can store the energy before firing or losing that energy) to reach this power? You will need to make a reasonable assumption about the collecting area of a fully dilated pupil.

Explanation / Answer

(a)

P = E/t

= nhf/t

n/t = P/ hf

= 10^-12 W/ 6.63 * 10^-34 Js(100 * 10^6 Hz)

=1.5 * 10^13 photons/s

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P = E/t

I/A = nhc/ lamda/t

n = (I*A)(lamda *t)/ hc

here I consider diameter of pupil eye is 8 mm

= ( 10^-12* 4pi ( 8* 10^-3 m/2)^2) ( 550 * 10^-9 m)( 0.033)/ 6.63 * 10^-34 ( 3.0* 10^8 m/s)

=18.33 photons

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