Question

A stationary hydrogen atom deexcites from first excited state to ground state. Find recoil speed of hydrogen atom up to nearest integer value.
(mass of hydrogen atom = $1.8 \times 10^{-27}$ $kg$)

Answer 1

|ΔE_0| = (-13.6 \left\\{1-\frac{1}{4}\right\\} )ev
$|ΔE| = 10.2\ ev$
$λ=\frac{12400}{10.2} × 10^{-10}\ m$
$ρ=\frac{h}{λ}$
$=\frac{6.63 × 10^{-34} × 10.2}{12400 × 10^{-10}}$
$\because mv=\frac{h}{λ}$
$\therefore 1.8 × 10^{-27}$
$v = \frac{6.63×10.2×10^{-34}}{12400 × 10^{-10}}$
$v =\frac{6.63 × 10.2}{12400×1.8} × 10^3$
$=\frac{6.63 × 102}{124 × 1.8}$
$= 3.02 ≈ 3\ m/s$
$\therefore$ , Recoil speed of hydrogen atom is 3 m/s