Question

A source of monochromatic radiation of wavelength $400\, nm$ provides $1000\, J$ 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 $400\, nm$ is sufficient for ejection of electron from the surface of sodium metal. The value of $x$ is____
(Nearest integer) $\left(h=6.626 \times 10^{-34} J_{S}\right)$

Answer 1

Total energy provided by
Source per second $=\frac{1000}{10}=100\, J$
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 $=\frac{100}{\frac{6.626 \times 10^{-34} \times 3 \times 10^{8}}{400 \times 10^{-9}}}$
$=\frac{400 \times 10^{-7} \times 10^{26}}{6.626 \times 3}$
$=\frac{40 \times 10^{-20}}{6.626 \times 3}$
$=2.01 \times 10^{20}$