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Question

Ultraviolet light of wavelength 99 nm falls on a metal plate of work function 1.0 eV. Find the wavelength of the fastest photoelectron emitted. (melectron=9.1×1031 kg and h=6.6×1034 Js)

A
0.72 nm
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B
0.36 nm
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C
10 nm
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D
0.1 nm
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Solution

The correct option is B 0.36 nm
Given, λ=99 nm ; ϕ0=1.0 eV

From, Einstein's photo electric equation,

KEmax=hcλϕ0

=(6.6×1034)×(3×108)99×1091.0×1.6×1019=20×10191.6×1019

=18.4×1019 J

de-Broglie wavelength of the particles will be,

λ=h2mKE=6.6×10342×(9.1×1031)×18.4×1019

=6.6×103418.29×1025=0.36×109 m=0.36 nm

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, (B) is the correct answer.

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