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# A photocell is operating in saturation mode with a aphotocurrent 4.8mA when a monochromatic radiation of wavelength $\;3000A^{0}\;$ and power 1mW is incident. When another monochromatic radiation of wavelength $\;1650A^{0}\;$ and power 5mW is incident , it is observed that maximum velocity of photoelectron generation per incident to be same for both cases . Than the threshold wavelength for cell is : The efficiency of photoelectron generation will be

$(a)\;5 \% \qquad(b)\;10 \% \qquad(c)\;15 \% \qquad(d)\;20 \%$

Answer : (a) $\;5 \%$
Energy of a photon is first case $\;\large\frac{12400}{3000}=4.13eV$
$or\;\varepsilon_{1}=6.6\times10^{-19}J$
Rate of incident protons $\;\large\frac{P_{1}}{\varepsilon_{1}}=\large\frac{10^{-3}}{6.6\times10^{-19}}=1.52\times10^{15}\;$ per second
No.of electrons ejected = $\;\large\frac{4.8times10^{-3}}{1.6\times10^{-19}}\;$ per second
$=3\times10^{16}\;$ per second
Efficiency of photoelectron generation = $\;\large\frac{1.52\times10^{15}}{3\times10^{16}}\times100$
$=5 \% \;.$