Hydrogen atom from excited state comes to the ground by emitting a...

When an electron jumps from a ${n}^{th}$ orbit to ground state, using Rydberg formula,

$\dfrac{1}{\lambda} = R\left(\dfrac{1}{{{n}_{1}}^{2}} - \dfrac{1}{{{n}_{2}}^{2}}\right)$

In this case, ${n}_{1} = 1$ and ${n}_{2} = n$. Therefore,

$⇒ \dfrac{1}{\lambda} = R\left(\dfrac{1}{{1}^{2}} - \dfrac{1}{{n}^{2}}\right) ⇒ n = \sqrt{\dfrac{\lambdaR}{\lambdaR - 1}}$