Department of Pre-University Education, Karnataka course PUC Karnataka Science Class 12
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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. - Physics

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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.)

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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Solution 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. Concept: Electromagnetic Spectrum.
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