CBSE 2026 · Region 2 · Set 2 · Q23 · 3 marks
Calculate the de Broglie wavelength associated with an electron revolving in the second excited state of hydrogen atom. The ground state energy of the hydrogen atom is -$\displaystyle 13.6$ eV. Take $\displaystyle \mathrm{m}_{\mathrm{e}}=9 \times 10^{-31} \mathrm{~kg}, \mathrm{~h}=6.6 \times 10^{-34} \mathrm{~J}$.s.
Marking-scheme solution
Total energy of the electron in the second excited state of the hydrogen atom: $\displaystyle \mathrm{E}_{n}=\dfrac{-13.6}{n^{2}} \mathrm{eV}$
$\displaystyle \mathrm{E}_{3}=\dfrac{-13.6}{3^{2}} \mathrm{eV}$
$\displaystyle \mathrm{E}_{3}=-1.51 \mathrm{eV}$
$\displaystyle \therefore$ Kinetic energy of the electron in this state, $\displaystyle \mathrm{K}=1.51 \mathrm{eV}$
de Broglie wavelength $\displaystyle \lambda=\dfrac{h}{\sqrt{2 m \mathrm{~K}}}$
$\displaystyle =\dfrac{6.6 \times 10^{-34}}{\sqrt{2 \times 9 \times 10^{-31} \times 1.51 \times 1.6 \times 10^{-19}}}$
$\displaystyle \lambda \approx 10^{-9} \mathrm{~m}=1 \mathrm{~nm}$
AtomsDE Broglie’s Explanation of Bohr’s Second Postulate of QuantisationApplyshort_answermedium
More from Atoms
- The radius of the n^ th orbit in Bohr model of hydrogen atom is proportional to2023 · asked 4×
- Assertion: An alpha particle is moving towards a gold nucleus. The impact parameter is maximum for the…2024 · asked 3×
- Draw the graph showing the variation of the number (N) of scattered alpha particles with scattering angle ( θ…2022 · asked 3×
- Hydrogen atom initially in the ground state, absorbs a photon which excites it to n=5 level. The wavelength…2023 · asked 3×
- The transition of electron that gives rise to the formation of the second spectral line of the Balmer series…2024 · asked 3×
- Draw the graph showing variation of scattered particles detected ( N ) with the scattering angle ( θ ) in…2024 · asked 3×
- Energy levels A, B and C of an atom correspond to increasing values of energy i.e. E A<E B<E C. Let λ 1, λ 2…2024 · asked 3×
- In Balmer series of hydrogen atom, as the wavelength of spectral lines decreases, they appear2024 · asked 3×
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.