We are introduced to the Bohr model of atom one time or the other in the course of physics. This model has its place in the history of quantum mechanics and particularly in explaining the structure of an atom. It has become a milestone since Bohr introduced the revolutionary idea of definite energy orbits for the electrons, contrary to the classical picture requiring an accelerating particle to radiate. Bohr also introduced the idea of quantisation of angular momentum of electrons moving in definite orbits. Thus, it was a semi-classical picture of the structure of atom.
Now with the development of quantum mechanics, we have a better understanding of the structure of atom. Solutions of the Schrodinger wave equation assign a wave-like description to the electrons bound in an atom due to attractive forces of the protons.
An orbit of the electron in the Bohr model is the circular path of motion of an electron around the nucleus.
- Bohr model is valid only for one-electron atom/ions; an energy value, assigned to each orbit, depends on the principal quantum number \( n \) in this model. We know that energy associated with a stationary state of an electron depends on \( n \) only. For one-electron atoms/ions. For a multi-electron atom/ion, this is not true.
According to Bohr postulates, wavelength of spectral lines can't be determined for
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Na
Bohr's model is valid only for one-electron atoms/ions (hydrogen-like species). For them the energy levels are
\( \displaystyle E_{n} = -\frac{13.6\,Z^{2}}{n^{2}}\,\mathrm{eV} \)
and the wavelengths of the spectral lines follow from the differences of these levels. In a multi-electron atom the electrons repel one another, the energy no longer depends on \( n \) alone, and Bohr's postulates cannot give the wavelengths.
Option (1) Na — Many-electron atom. Sodium has 11 electrons, so Bohr's model cannot determine its spectral wavelengths.
Option (2) \( \mathrm{Li^{++}} \) — One-electron ion. \( \mathrm{Li^{++}} \) (\( Z = 3 \)) has a single electron, so Bohr's formula applies with \( Z = 3 \).
Option (3) \( \mathrm{He^{+}} \) — One-electron ion. \( \mathrm{He^{+}} \) (\( Z = 2 \)) has a single electron, so Bohr's formula applies with \( Z = 2 \).
Option (4) H — One-electron atom. Hydrogen is the atom for which Bohr's model was built.
NCERT (2026-27):
De Broglie’s Explanation of Bohr’s Second Postulate of Quantisation – “… (i) The Bohr model is applicable to hydrogenic atoms. It cannot be extended even to mere two electron atoms such as helium.”
De Broglie’s Explanation of Bohr’s Second Postulate of Quantisation – “… * Hydrogenic atoms are the atoms consisting of a nucleus with positive charge +Ze and a single electron, where Z is the proton number.”