Answer to Question #121930 in Quantum Mechanics for Moel Tariburu

Question

Suppose an atom of Osmium at rest emits an X-ray photon of energy 6.8 keV. Calculate the
“recoil” momentum and kinetic energy of the atom

Answer 1

According to the conservation of momentum law (https://en.wikipedia.org/wiki/Conservation_of_momentum) the module of momentum of atom is equal to the module of momentum of the photon.

The momentum of photon can be calculated as $p=\dfrac{E}{c} = \dfrac{6.8\cdot10^3\cdot1.6\cdot10^{-19}\,\mathrm{J}}{3\cdot10^8\,\mathrm{m/s}} = 3.63\cdot10^{-24}\,\mathrm{kg\cdot m/s}.$ The same value has the atom.

Kinetic energy is $\dfrac{mv^2}{2} = \dfrac{p^2}{2m} = \dfrac{(3.63\cdot10^{-24}\,\mathrm{kg\cdot m/s})^2}{2\cdot190.23\cdot1.66\cdot10^{-27}\,\mathrm{kg}} = 2.1\cdot10^{-23}\,\mathrm{J}.$