Dual Nature Of Radiation And Matter Ques 22
22. Light of wavelength $500$ $ nm$ is incident on a metal with work function $2.28$ $ eV$. The wavelength of the emitted electron is:
[2015 RS]
(a) $<2.8 \times 10^{-9} $ $m$
(b) $\geq .2 .8 \times 10^{-9} $ $m$
(c) $\leq 2.8 \times 10^{-12} $ $m$
(d) $<2.8 \times 10^{-10} $ $m$
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Answer:
Correct Answer: 22.(b)
Solution:
- (b) Given : Work function $\phi$ of metal $=2.28 $ $eV$
Wavelength of light $\lambda=500$ $ nm=500 \times 10^{-9}$ $ m$
$KE _{\text{max }}=\frac{hc}{\lambda}-\phi$
$KE _{\text{max }}=\frac{6.6 \times 10^{-34} \times 3 \times 10^{8}}{5 \times 10^{-7} \times 1.6 \times 10^{-19}}-2.28$
$KE _{\text{max }}=2.48-2.28=0.2 $ $ev$
$\lambda _{\text{min }}=\frac{h}{p}=\frac{h}{\sqrt{2 m(KE) _{\max }}}$
$=\frac{\frac{20}{3} \times 10^{-34}}{\sqrt{2 \times 9 \times 10^{-31} \times 0.2 \times 1.6 \times 10^{-19}}}$
$\lambda _{\text{min }}=\frac{25}{9} \times 10^{-9}$
$=2.80 \times 10^{-9}$ $ nm \quad \therefore \lambda \geq 2.8 \times 10^{-9} $ $m$
BETA
