Q. When an electron jumps from a level $n = 4$ to $n = 1,$ momentum of the recoiled hydrogen atom will be
A) $6.8 \times 10^{- 27}kg\ –{ms}^{- 1}$
B) $12.75 \times 10^{- 19}kg\ –{ms}^{- 1}$
C) $136 \times 10^{- 19}kg\ –{ms}^{- 1}$
D) zero
Explanation
(a) $E = E_{4} - E_{1} = - \frac{13.6}{4^{2}}—\left( - \frac{13.6}{1^{2}} \right)$
$= - 0.85 + 13.6 = 12.75\ eV$
$= 12.75 \times 1.6 = 10^{- 14}\ J$
$P = \frac{E}{c} = \frac{12.75 \times 1.6 \times 10^{- 19}}{3 \times 10^{8}}$
$= 6.8 \times 10^{- 27}kg\ ms^{- 1}$
This must be the momentum of recoiled hydrogen atom (in opposite direction)
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.