Find the number of photons emitted per second | vedclass

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Question

(A) The power $P$ of the transmitter is given by $P = nE$,where $n$ is the number of photons emitted per second and $E$ is the energy of a single phot

Vedclass · Accepted Answer

$2.5 	imes 10^{31} \ s^{-1}$

Vedclass · Answer

(A) The power $P$ of the transmitter is given by $P = nE$,where $n$ is the number of photons emitted per second and $E$ is the energy of a single photon.Energy of a single photon is $E = \frac{hc}{\lambda}$.Therefore,$P = n \frac{hc}{\lambda}$,which implies $n = \frac{P\lambda}{hc}$.Given: $P = 10 \ kW = 10^4 \ W$,$\lambda = 500 \ m$,$h = 6.626 	imes 10^{-34} \ J \cdot s$,and $c = 3 	imes 10^8 \ m/s$.Substituting the values:$n = \frac{10^4 	imes 500}{6.626 	imes 10^{-34} 	imes 3 	imes 10^8}$$n = \frac{5 	imes 10^6}{19.878 	imes 10^{-26}}$$n \approx 0.2515 	imes 10^{32} \ s^{-1} = 2.515 	imes 10^{31} \ s^{-1}$.Rounding to the nearest option,we get $2.5 	imes 10^{31} \ s^{-1}$.

Find the number of photons emitted per second by a $10 \ kW$ radio transmitter operating at a wavelength of $500 \ m$.

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