A free atom of iron emits `K_alpha` X-rays of energy 6.4 keV. Calculate the recoil kinetic energy of the atom. Mass of and iron atom `= 9.3 xx 10 ^(-26) kg`.

Explanation

`Here energy of photon =E `
`E=6.4KeV=6.4xx10^3eV`
Momentum of photon
` =E/c=(6.4xx10^3)/(3xx10^8) `
` =3.41xx10^-24kgm//sec `
According to collision theory
Momentum of Photon
` =Momentumof Atom `
` :.Momentum of Atom `
` P=3.14xx10^-24kgm//sec `
` :. Recoil K.E. of atom `
` P^2/(2M) `
` (3.41xx10^-24)^2(eV)/((20)9.3xx10^-26xx1.6xx10^-19)=3.9eV `
` [1 Joule=1.6xx10^-19eV]`