Determine the number of electrons emitted per square meter per second.

1.47 \times 10^{9} m^{- 2} s^{- 1}

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1.47 \times 10^{10} m^{- 2} s^{- 1}

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2.47 \times 10^{10} m^{- 2} s^{- 1}

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2.47 \times 10^{9} m^{- 2} s^{- 1}

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Solution

The correct option is B $1.47 \times 10^{10} m^{- 2} s^{- 1}$
Intensity of light falling $I_{o} = 10^{- 8} W / m^{2}$
Wavelength of light $λ = 365 \times 10^{- 9} m$
Absorption coefficient $a = 0.8$
Thus intensity of light absorbed $I = a I_{o} = 0.8 \times 10^{- 8} W / m^{2}$
Energy of one photon $E = \frac{h c}{λ}$
So, number of photons absorbed per sq.meter per second $N = \frac{I}{E} = \frac{I λ}{h c}$
$∴$ $N = \frac{(0.8 \times 10^{- 8}) (365 \times 10^{- 9})}{(6.62 \times 10^{- 34}) (3 \times 10^{8})} =$ $1.47 \times 10^{10}$ photons $m^{- 2} s^{- 1}$
Since one photon ejects one electron from the surface, so number of electron emitted is $1.47 \times 10^{10}$ electrons $m^{- 2} s^{- 1}$ .

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