Find the number of photons emitted per second | vedclass

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(A) The energy of a single photon is given by $E = \frac{hc}{\lambda}$.Given: $P = 25 	ext{ W}$, $\lambda = 6600 	ext{ Å} = 6600 	imes 10^{-10} 	e

Vedclass · Accepted Answer

$\frac{25}{2} 	imes 10^{19}, 0.4 	ext{ A}$

Vedclass · Answer

(A) The energy of a single photon is given by $E = \frac{hc}{\lambda}$.Given: $P = 25 	ext{ W}$, $\lambda = 6600 	ext{ Å} = 6600 	imes 10^{-10} 	ext{ m}$, $h = 6.63 	imes 10^{-34} 	ext{ J}·	ext{s}$, $c = 3 	imes 10^8 	ext{ m/s}$.The number of photons emitted per second $(n)$ is $n = \frac{P}{E} = \frac{P\lambda}{hc}$.$n = \frac{25 	imes 6600 	imes 10^{-10}}{6.63 	imes 10^{-34} 	imes 3 	imes 10^8} \approx 8.3 	imes 10^{19} 	ext{ photons/s}$.Given $3 \%$ efficiency, the number of photoelectrons produced per second is $n' = 0.03 	imes n$.The photoelectric current $I = n' 	imes e = 0.03 	imes n 	imes 1.6 	imes 10^{-19} 	ext{ C}$.$I = 0.03 	imes 8.3 	imes 10^{19} 	imes 1.6 	imes 10^{-19} \approx 0.4 	ext{ A}$.

Find the number of photons emitted per second by a $25 \text{ W}$ source of monochromatic light of wavelength $6600 \text{ Å}$. What is the photoelectric current assuming $3 \%$ efficiency for the photoelectric effect?

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