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(B) The energy of incident photons is $E = 4.8 eV$ and the work function of the sphere is $\phi = 2.8 eV$. Photoelectric emission stops when the poten

Vedclass · Accepted Answer

$125$

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(B) The energy of incident photons is $E = 4.8 eV$ and the work function of the sphere is $\phi = 2.8 eV$. Photoelectric emission stops when the potential of the sphere $V$ reaches a value such that the kinetic energy of the emitted electrons is zero. This occurs when $eV = E - \phi = 4.8 eV - 2.8 eV = 2.0 eV$,so $V = 2.0 V$.The capacitance of a sphere of radius $R = 9 mm = 9 	imes 10^{-3} m$ is $C = 4\pi\epsilon_0 R = \frac{R}{k} = \frac{9 	imes 10^{-3}}{9 	imes 10^9} = 10^{-12} F$.The charge $Q$ required to reach potential $V$ is $Q = CV = 10^{-12} F 	imes 2.0 V = 2 	imes 10^{-12} C$.The number of electrons emitted is $n = \frac{Q}{e} = \frac{2 	imes 10^{-12}}{1.6 	imes 10^{-19}} = 1.25 	imes 10^7$.Since the rate of emission is $10^5$ electrons per second,the time taken is $t = \frac{n}{	ext{rate}} = \frac{1.25 	imes 10^7}{10^5} = 125 s$.

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