Dual Nature of Radiation and Matter - Result Question 25

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27. Light of wavelength $500 nm$ is incident on a metal with work function $2.28 eV$. The wavelength of the emitted electron is:

======= ####27. Light of wavelength $500 nm$ is incident on a metal with work function $2.28 eV$. The wavelength of the emitted electron is:

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed:content/english/neet-pyq-chapterwise/physics/dual-nature-of-radiation-and-matter/dual-nature-of-radiation-and-matter—result-question-25.md (a) $<2.8 \times 10^{-9} m$

(b) $\geq .2 .8 \times 10^{-9} m$

(c) $\leq 2.8 \times 10^{-12} m$

(d) $<2.8 \times 10^{-10} m$

[2015 RS]

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Answer:

Correct Answer: 27. (b)

Solution:

  1. (b) Given : Work function $\phi$ of metal $=2.28 eV$ Wavelength of light $\lambda=500 nm=500 \times 10^{-9} m$

$KE _{\text{max }}=\frac{hc}{\lambda}-\phi$

$KE _{\text{max }}=\frac{6.6 \times 10^{-34} \times 3 \times 10^{8}}{5 \times 10^{-7} \times 1.6 \times 10^{-19}}-2.28$

$KE _{\text{max }}=2.48-2.28=0.2 ev$

$\lambda _{\text{min }}=\frac{h}{p}=\frac{h}{\sqrt{2 m(KE) _{\max }}}$

$=\frac{\frac{20}{3} \times 10^{-34}}{\sqrt{2 \times 9 \times 10^{-31} \times 0.2 \times 1.6 \times 10^{-19}}}$

$\lambda _{\text{min }}=\frac{25}{9} \times 10^{-9}$

$=2.80 \times 10^{-9} nm \quad \therefore \lambda \geq 2.8 \times 10^{-9} m$