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Question

A free atom of iron emits Kα X-rays of energy 6.4 keV. Calculate the recoil kinetic energy of the atom.
Mass of an iron atom =9.3×1026 kg.

A
3.9×104 eV
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B
5×104 eV
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C
2.3×104 eV
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D
8.3×104 eV
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Solution

The correct option is A 3.9×104 eV
Given energy of photon,

E=6.4 KeV=6.4×103 eV

Momentum of photon,

p=Ec=6.4×103×1.6×10193×108

p=3.41×1024 kg m/s

According to collision theory,

momentum of photon = momentum of atom

Recoil KE of atom will be,

KE=p22m=(3.41×1024)2(2)(9.3×1026)

KE=6.25×1023 J

KE=6.25×10231.6×1019=3.9×104 eV

Hence, option (A) is correct.
Why this question ?
Concept:- This question helps in solving the problems having multi concepts ( X-rays and conservation of momentum) .

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