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  4. Light of wavelength 5000 mathringA and intensity 39.8 W m -2 is incident on a metal surface. If only 1 % photons of incident light emit photoelectrons, then the number of electrons emitted per second per unit area from the surface will be nearly

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Q. Light of wavelength $5000\,\mathring{A}$ and intensity $39.8\, W m ^{-2}$ is incident on a metal surface. If only $1 \%$ photons of incident light emit photoelectrons, then the number of electrons emitted per second per unit area from the surface will be nearly

Dual Nature of Radiation and Matter

Solution:

Energy of photon
$E=\frac{h c}{\lambda}=\frac{1242\, eV - nm }{500 nm }=2.484 \,eV $
$=2.484 \times 1.6 \times 10^{-19} J =4 \times 10^{-19} J $
$\text { Intensity }=39.8 \frac{ W }{ m ^{2}}=\frac{39.8 J / s }{ m ^{2}} $
Number of photons falling per second per unit area
$=\frac{39.8}{4 \times 10^{-19}\left( m ^{2} s \right)}\left(\frac{ J }{ J }\right)=1 \times 10^{20}$
$1 \%$ of photon eject photoelectron $=1 \% \times 10^{20}=10^{18}$