A small plate of a metal is placed at a distance of $2 m$ from a monochromatic light source of wavelength $4.8 \times 10^{- 7} m$ and power 1 watt. The light falls normally on the plate. Find the number of photons striking the metal plate per square meter per second.

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$9 \times 10^{16} m^{- 2} s^{- 1}$

$20 \times 10^{16} m^{- 2} s^{- 1}$

$8 \times 10^{16} m^{- 2} s^{- 1}$

$4.82 \times 10^{16} m^{- 2} s^{- 1}$

answer is D.

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Detailed Solution

$E = \frac{h c}{λ} = \frac{(6.6 \times 10^{- 34}) (3 \times 10^{8})}{(4.8 \times 10^{- 7})} = 4.125 \times 10^{- 19} J$

Number of photons striking the metal plate per square meter per second is

$n = (\frac{P}{E}) (\frac{1}{4 π r^{2}})$

$\Rightarrow n = (\frac{1}{4.125 \times 10^{- 19}}) \frac{1}{(4 π) (2)^{2}} = 4.82 \times 10^{16} m^{- 2} s^{- 1}$

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