\(\frac{1}{\lambda}=R\left[\frac{1}{n_{f}^{2}}-\frac{1}{n_{i}^{2}}\right]\)

Here, \(n_{f}=1, n_{i}=5\)

\(\therefore \quad \frac{1}{\lambda}=R\left[\frac{1}{1^{2}}-\frac{1}{5^{2}}\right]=R\left[\frac{1}{1}-\frac{1}{25}\right]=\frac{24}{25} R\)

According to conservation of linear momentum, we

get Momentum of photon \(=\) Momentum of atom

\(\frac{h}{\lambda}=m v \text { or } v=\frac{h}{m \lambda}=\frac{h}{m}\left(\frac{24 R}{25}\right)=\frac{24 h R}{25 m}\)