Question

A free atom of iron emits Kα 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

Answer is 3.9 eV

Explanation:

• Here energy of photon = E

• Mass of an iron atom = $9.3 \times 10 ^{-26}$ kg  

• E = 6.4 KeV = $6.4 \times 10^3 eV$

• Momentum of Photon = $\frac {E}{C}$

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

= $3.41 \times 10^{-24} msec^-^1$

• According to collision theory of momentum of photon = momentum of atom  

• Momentum of Atom = P = $3.41 \times 10^{-24}\ msec^-^1$

Recoil K.E of atom = $\frac {P^2}{2m}$

= $\frac {(3.41 \times 10^{-24})^2}{2(9.3 \times 10 ^{-26} \times 1.6 \times 10^{-19})}$

= $3.9\ eV (1\ Joule = 1.6 \times 10^{-19})$