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Q.
The energy required to ionise a hydrogen like ion in its ground state is 9 Rydbergs. What is the wavelength of the radiation emitted when the electron in this ion jumps from the second excited state to the ground state ?
$
\begin{array}{l}
E _{ n }=-\frac{\text { Ionisation energy }}{ n ^{2}} \\
=\frac{- q R }{ n ^{2}}
\end{array}
$
now, when it jumps, the released energy will be
$
\begin{array}{l}
E _{2}- E _{1}=- qR \left(\frac{1}{9}-1\right) \\
=8 R
\end{array}
$
$
\begin{array}{l}
\text { Now, } E =\frac{ hc }{\lambda}=8 R \\
\lambda=\frac{ hc }{8 R } \\
=\frac{6.64 \times 10^{-34} \times 3 \times 10^{8}}{8 \times 2.2 \times 10^{-18}} \\
=11.31 nm \\
\approx 11.4 nm
\end{array}
$