CBSE 2022 · Region 1 · Set 2 · Q9 · 3 marks
(a)Sketch the energy level diagram for hydrogen atom.(b)Find the ratio of the longest and the shortest wavelength in Lyman series in hydrogen atom.
(a)
Sketch the energy level diagram for hydrogen atom.
(b)
Find the ratio of the longest and the shortest wavelength in Lyman series in hydrogen atom.
Marking-scheme solution
i) Hydrogen atom energy level diagram
(ii)
$\displaystyle \frac{1}{\lambda}=R\left\lfloor\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right\rfloor$
For longest wavelength in Lyman series
$$n_{$\displaystyle 1$}=$\displaystyle 1$, n_{$\displaystyle 2$}=$\displaystyle 2$
$$\begin{aligned}
& \frac{1}{\lambda_{$\displaystyle 1$}}=R\left[\frac{1}{1^{2}}-\frac{1}{2^{2}}\right]=R\left[1-\frac{1}{4}\right]=\frac{3}{4} R
& \therefore \lambda_{$\displaystyle 1$}=\frac{4}{3 R}
\end{aligned}
$$For shortest wavelength in Lyman Series
$$n_{$\displaystyle 1$}=$\displaystyle 1$, n_{$\displaystyle 2$}=\infty
$$\begin{aligned}
& \frac{1}{\lambda_{$\displaystyle 2$}}=R\left[\frac{1}{1^{2}}-\frac{1}{\infty^{2}}\right]=R[$\displaystyle 1$-$\displaystyle 0$]=R
& \therefore \lambda_{$\displaystyle 2$}=\frac{1}{R}
\end{aligned}
AtomsBohr Model of the Hydrogen AtomApplyshort_answermedium
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CBSE Class 12 Physics past-paper question from the 2022board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.