Answer to Question #122039 in Quantum Mechanics for komal

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

As,system has initial momentum is zero and no external interaction there,Momentum of the system is conserved.

Therefore, momentum

$$p_{os}+p_{\gamma}=0 ​$$

We have given that, emitted photon has energy is $8.6keV$

Since,

$$E_{\gamma}=p_{\gamma}c\\ \implies p_{\gamma}=\frac{E_{\gamma}}{c}=8.6keV/c$$

Thus,

$$p_{os}=-8.6keV/c$$

Kinetic energy is

$$K=\frac{p^2}{2m}$$

​

Hence,

$$K_{os}=2.088\times 10^{-4}eV$$