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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 × 10−26 kg.
(Use Planck constant h = 6.63 × 10-34 Js= 4.14 × 10-15 eVs, speed of light c = 3 × 108 m/s.)
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Solution
Here, energy of photon = E
E = 6.4 KeV = 6.4 × 103 eV
Momentum of photon
`= E/c = (6.4 xx 10^3)/(3 xx 10^8)`
`= 3.41 xx 10^-24 "kgm/sec"`
According to collision theory,
Momentum of photon = Momentum of atom
∴ Momentum of atom, P = 3.41 × 10−24 kgm/sec
Recoil KE of atom = P2/2M
`= ((3.41 xx 10^-24)^2 eV)/((20)9.3 xx 10^-26 xx 1.6 xx 10^-19) = 3.9 "eV"`
[1 Joule = 1.6 × 10−19 eV]
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