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Physics · 2026 · 3 marks
CBSE 2026 · Region 2 · Set 1 · Q26
(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…
(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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