Thank you for reporting, we will resolve it shortly
Q.
In the hydrogen atom spectrum, let $E_{1}$ and $E_{2}$ are energies for the transition $n=2 \rightarrow n=1$ and $n=3 \rightarrow$ $n=2$ respectively. The ratio $E2/E1$ is
TS EAMCET 2020
Solution:
Energy value of nth state for $H$-electron is
$E_{n}=\frac{E_{1}}{n^{2}}$
Now, given transitions are
Energy radiated in transition $n=3$ to $n=2$ is
$E_{2}=\frac{E_{1}}{9}-\frac{E_{1}}{4}=\frac{-5 E_{1}}{36}$
Also, energy radiated in transition $n=2$ to $n=1$ is
$E_{1}=\frac{E_{1}}{4}-\frac{E_{1}}{1}=\frac{-3 E_{1}}{4}$
Hence, ratio of $\frac{E_{2}}{E_{1}}$ is $\frac{5}{27}$.
