A source of monochromatic radiation

Question:

A source of monochromatic radiation of wavelength $400 \mathrm{~nm}$ provides $1000 \mathrm{~J}$ of energy in 10 seconds. When this radiation falls on the surface of sodium, $x \times 10^{20}$ electrons are ejected per second. Assume that wavelength $400 \mathrm{~nm}$ is sufficient for ejection of electron from the surface of sodium metal. The value of $x$ is________

(Nearest integer)

$\left(\mathrm{h}=6.626 \times 10^{-34} \mathrm{Js}\right)$

Solution:

Total energy provided by

Source per second $=\frac{1000}{10}=100 \mathrm{~J}$

Energy required to eject electron $=\frac{h c}{\lambda}$

$=\frac{6.626 \times 10^{-34}}{400 \times 10^{-9}} \times 3 \times 10^{8}$

Number of electrons ejected

$=\frac{100}{\frac{6.626 \times 10^{-34} \times 3 \times 10^{8}}{400 \times 10^{-9}}}$

$=\frac{400 \times 10^{-7} \times 10^{26}}{6.626 \times 3}$

$=\frac{40 \times 10^{-20}}{6.626 \times 3}$

$=2.01 \times 10^{20}$

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