A source of monochromatic radiation… - JEE Main 2021 Chemistry PYQ

JEE Main 2021 — Chemistry Physical Chemistry

2021integerhard

A source of monochromatic radiation wavelength $400\mathrm{nm}$ provides $1000J$ 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)

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

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Held on 25 Jul 2021 · Verified 6 Jul 2026.

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Solution

Total energy provided by

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

Energy required to eject electron $=\frac{\mathrm{hc}}{\lambda }$

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

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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