A stationary hydrogen atom undergoes a transition from $n=5$ to $n=4$. Recoil speed of the atom is $(R=$…
A stationary hydrogen atom undergoes a transition from $n=5$ to $n=4$. Recoil speed of the atom is $(R=$ Rydberg constant, $h=$ Planck's constant and $m=$ mass of the proton).
$\frac{R h}{m}$
$\frac{9 m}{400 R h}$
$\frac{9 R h}{400 m}$
$\frac{7 R h}{400}$
Solution
For transition $5 \rightarrow 4$,
Momentum of photon, $p=\frac{h}{\lambda}=h R\left(\frac{1}{16}-\frac{1}{25}\right)$ and recoil speed, $v=\frac{p}{m}=\frac{h R\left(\frac{1}{16}-\frac{1}{25}\right)}{m}=\frac{9 h R}{400 m}$