A light bulb emits 5% of its energy as visibl | vedclass

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(A) Given: Power $P = 100 \ W$,Efficiency $\eta = 5\% = 0.05$,Wavelength $\lambda = 5.6 	imes 10^{-5} \ cm = 5.6 	imes 10^{-7} \ m$.The power emitte

Vedclass · Accepted Answer

$1.4 	imes 10^{19}$

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(A) Given: Power $P = 100 \ W$,Efficiency $\eta = 5\% = 0.05$,Wavelength $\lambda = 5.6 	imes 10^{-5} \ cm = 5.6 	imes 10^{-7} \ m$.The power emitted as visible light is $P' = P 	imes \eta = 100 	imes 0.05 = 5 \ W$.The energy of one photon is $E = \frac{hc}{\lambda}$.The number of photons (quanta) emitted per second $n$ is given by $n = \frac{P'}{E} = \frac{P' \lambda}{hc}$.Substituting the values: $n = \frac{5 	imes 5.6 	imes 10^{-7}}{6.63 	imes 10^{-34} 	imes 3 	imes 10^8}$.$n = \frac{28 	imes 10^{-7}}{19.89 	imes 10^{-26}} \approx 1.407 	imes 10^{19} 	ext{ quanta/sec}$.

$A$ light bulb emits $5\%$ of its energy as visible light. How many quanta are emitted per second by a $100 \ W$ lamp? (Assume the wavelength of visible light is $5.6 \times 10^{-5} \ cm$)

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