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Question

When electromagnetic radiation of wavelength 300 nm falls on the surface of sodium, electrons are emitted with a kinetic energy of 1.68×105J mol1. What is the maximum wavelength that will cause a photoelectron to be emitted?

A
λ=320 nm
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B
λ=449.7 nm
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C
λ=526 nm
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D
λ=518 nm
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Solution

The correct option is D λ=518 nm
The energy of a 300 nm photon =hv=hcλ
=6.626×1034 J s×3.0×108 m s1300×109 m
=6.626×1019 J

The energy of one mole of photon =6.626×1019 J×6.022×1023 mol1
=3.99×105 J mol1

The minimum energy needed to remove a mole of electrons from sodium = Energy of photons - Kinetic energy of electrons
=(3.991.68)×105 J mol1
=2.31×105 J mol1

The minimum energy for one electron =2.31×105 J mol16.022×1023 mol1
=3.84×1019 J

λ=hcE
=6.626×1034 J s×3.0×108 m s13.84×1019 J
=5.18×107 m=518 nm

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