Question

A free atom of iron emits K_α 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.)

Answer 1

Here, energy of photon = E

E = 6.4 KeV = 6.4 × 10³ eV

Momentum of photon

${\displaystyle =\frac{E}{c}=\frac{6.4\times {10}^3}{3\times {10}^8}}$

${\displaystyle =3.41\times {10}^{-24} \text{kgm/sec}}$

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

${\displaystyle =\frac{{(3.41\times {10}^{-24})}^{2}eV}{\left(20\right)9.3\times {10}^{-26}\times 1.6\times {10}^{-19}}=3.9 \text{eV}}$

[1 Joule = 1.6 × 10⁻¹⁹ eV]