✓ Board-verified
Physics · 2025 · 3 marks
CBSE 2025 · Region 7 · Set 1 · Q27
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 n^th…
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 ($\displaystyle 1$) &
\[\mathrm{r}=\mathrm{n}^{2}\left(\frac{\mathrm{~h}}{2 \pi}\right)^{2} \frac{4 \pi \varepsilon_{0}}{\mathrm{me}^{2}}
\]More from Atoms
- Define the term - Distance of closest approach. How will it be affected, for an α - particle, if kinetic energy of the particle is doubled?2022
- Define the'distance of closest approach'. An α -particle of kinetic energy K is bombarded on a thin gold foil. Derive an expression for the'distance…2025
- State Bohr's postulate to explain stable orbits in a hydrogen atom. Prove that the speed with which the electron revolves in n^th orbit is…2022
- In Bohr's model of hydrogen atom, find the percentage change in the radius of its orbit when an electron makes a transition from n=3 state to n=2…2025
- Calculate the de Broglie wavelength associated with an electron revolving in the second excited state of hydrogen atom. The ground state energy of…2026
- State Bohr's first and second postulates. Use them to derive an expression for the radius of the n^th orbit in a hydrogen atom.2024
- Assertion: An alpha particle is moving towards a gold nucleus. The impact parameter is maximum for the scattering angle of 180^°. Reason (R): The…2024
- The radius of the n^th orbit in Bohr model of hydrogen atom is proportional to2023
CBSE Class 12 Physics past-paper question from the 2025 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.