CBSE 2025 · Region 7 · Set 1 · Q27 · 3 marks
Write the mathematical forms of three postulates of Bohr's theory of the hydrogen atom. Using them prove that, for an electron revolving in the $\displaystyle \mathrm{n}^{\text {th }}$ orbit,(a)the radius of the orbit is proportional to $\displaystyle \mathrm{n}^{2}$, and(b)the total energy of the atom is proportional to $\displaystyle \left(\frac{1}{\mathrm{n}^{2}}\right)$.
Write the mathematical forms of three postulates of Bohr's theory of the hydrogen atom. Using them prove that, for an electron revolving in the $\displaystyle \mathrm{n}^{\text {th }}$ orbit,
(a)
the radius of the orbit is proportional to $\displaystyle \mathrm{n}^{2}$, and
(b)
the total energy of the atom is proportional to $\displaystyle \left(\frac{1}{\mathrm{n}^{2}}\right)$.
Marking-scheme solution
Proving,
(a) radius of the orbit is proportional to \(\displaystyle \mathrm{n}^{2} \quad 1\)
(b) Total energy of the atom is proportional to \(\displaystyle 1 / \mathrm{n}^{2} \frac{1}{2}\)
Mathematical form of postulates of Bohr's Theory(i) \(\displaystyle \mathrm{E}_{\mathrm{n}}=\frac{-13.6}{\mathrm{n}^{2}} e \mathrm{~V}\)
Alternatively : Electron revolve in stable orbits with definite energy called stationary orbits.(ii) \(\displaystyle \mathrm{L}=\mathrm{mvr}=\frac{\mathrm{nh}}{2 \pi}\)
(iii) \(\displaystyle \mathrm{h} v=\mathrm{E}_{\mathrm{f}}-\mathrm{E}_{\mathrm{i}}\)
(a) \(\displaystyle \frac{\mathrm{mv}^{2}}{\mathrm{r}}=\frac{\mathrm{Ze}^{2}}{\mathrm{r}^{2}}\)
\[\mathrm{mvr}=\frac{\mathrm{nh}}{2 \pi}
\]
Solving ($\displaystyle 1$) &
\[\mathrm{r}=\mathrm{n}^{2}\left(\frac{\mathrm{~h}}{2 \pi}\right)^{2} \frac{4 \pi \varepsilon_{0}}{\mathrm{me}^{2}}
\]AtomsBohr Model of the Hydrogen AtomApplyshort_answerhard
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CBSE Class 12 Physics past-paper question from the 2025board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.