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.

Answer 1

Here, energy of photon = E
E = 6.4 KeV = 6.4 × 10³ eV
Momentum of photon
$$\begin{gathered} =\frac{\mathrm{E}}{c}=\frac{6.4\times {10}^3}{3\times {10}^8} \\ =3.41\times {10}^{-24}\mathrm{kgm}/\sec \end{gathered}$$
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
$=\frac{(3.41\times {10}^{-24}{)}^{2}e\mathrm{V}}{\left(20\right)9.3\times {10}^{-26}\times 1.6\times {10}^{-19}}=3.9e\mathrm{V}$
[1 Joule = 1.6 × 10⁻¹⁹ eV]