Atomic Structure: Practice Problem & Solution

Solution Explained:

To solve this problem, we apply the core principles of Atomic Structure. Understanding the underlying formula is key to arriving at the correct answer below:

Momentum of the emitted photon is $p = \frac{h}{\lambda} = hR(\frac{1}{1^2} - \frac{1}{5^2}) = hR(\frac{24}{25})$. By conservation of momentum, the recoil momentum of the atom is $mv = p = \frac{24hR}{25}$. Thus, velocity $v = \frac{24hR}{25m}$.