According to Bohr model of hydrogen atom, the angular momentum of an…

The correct answer is Option (4) → \( nh(2\pi)^{-1} \)

Bohr’s second postulate (quantisation condition): an electron can revolve only in those orbits for which its angular momentum is an integral multiple of \( h/2\pi \).

    \( \displaystyle L = mvr = \frac{nh}{2\pi} = nh(2\pi)^{-1}, \quad n = 1, 2, 3, \dots \)

NCERT (2026-27):
Bohr Model of the Hydrogen Atom – “… It was Niels Bohr (1885 – 1962) who made certain modifications in this model by adding the ideas of the newly developing quantum hypothesis. Niels Bohr studied in Rutherford’s laboratory for several months in 1912 and he was convinced about the validity of Rutherford nuclear model. Faced with the dilemma as discussed above, Bohr, in 1913, concluded that in spite of the success of electromagnetic theory in explaining large-scale phenomena, it could not be applied to the processes at the atomic scale. It became clear that a fairly radical departure from the established principles of classical mechanics and electromagnetism would be needed to understand the structure of atoms and the relation of atomic structure to atomic spectra. Bohr combined classical and early quantum concepts and gave his theory in the form of three postulates. These are :
(i) Bohr’s first postulate was that an electron in an atom could revolve in certain stable orbits without the emission of radiant energy, contrary to the predictions of electromagnetic theory. According to this postulate, each atom has certain definite stable states in which it can exist, and each possible state has definite total energy. These are called the stationary states of the atom.
(ii) Bohr’s second postulate defines these stable orbits. This postulate states that the electron revolves around the nucleus only in those orbits for which the angular momentum is some integral multiple of \( h/2\pi \) where \( h \) is the Planck’s constant (= \( 6.6\times10^{-34}\,\mathrm{J\,s} \)). Thus the angular momentum \( (L) \) of the orbiting electron is quantised. That is

    \( \displaystyle L = nh/2\pi \qquad (12.5) \)

(iii) Bohr’s third postulate incorporated into atomic theory the early quantum concepts that had been developed by Planck and Einstein. It states that an electron might make a transition from one of its specified non-radiating orbits to another of lower energy. When it does so, a photon is emitted having energy equal to the energy difference between the initial and final states. The frequency of the emitted photon is then given by

    \( \displaystyle h\nu = E_i - E_f \qquad (12.6) \)

where \( E_i \) and \( E_f \) are the energies of the initial and final states and \( E_i \gt E_f \).”