CBSE 2026 · Region 2 · Set 1 · Q26 · 3 marks
(a)State Bohr's second postulate and mention its significance.(b)Prove that, in Bohr model of hydrogen atom as principal quantum number n becomes large, the energy levels get closer and closer.
(a)
State Bohr's second postulate and mention its significance.
(b)
Prove that, in Bohr model of hydrogen atom as principal quantum number n becomes large, the energy levels get closer and closer.
Marking-scheme solution
(a)
The electron revolves around the nucleus only in those orbits for which angular momentum is some integral multiple of $\displaystyle \dfrac{\mathrm{h}}{2 \pi}$, where h is Planck's constant. (Alternatively: $\displaystyle L=n\left(\dfrac{h}{2 \pi}\right)$)
It defines stable / stationary orbits. (Alternatively: angular momentum is quantised)
(b)
$\displaystyle E_{n}=\dfrac{-13.6}{n^{2}} \mathrm{eV}$
For any two consecutive energy levels, the energy difference is $\displaystyle \Delta \mathrm{E}=\mathrm{E}_{n}-\mathrm{E}_{n-1}=13.6\left[\dfrac{1}{(n-1)^{2}}-\dfrac{1}{n^{2}}\right]$
$\displaystyle \Delta E=13.6 \dfrac{(2 n-1)}{n^{2}(n-1)^{2}}$
For large value of $\displaystyle n$: $\displaystyle \Delta E=\dfrac{27.2}{n^{3}} \mathrm{eV}$
Thus as $\displaystyle n$ increases, $\displaystyle \Delta E$ decreases, i.e. energy levels get closer and closer.
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CBSE Class 12 Physics past-paper question from the 2026board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.