In Bohr's model of hydrogen atom, which of the following is an integral multiple of \( \displaystyle\frac{h}{2\pi} \)?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Angular momentum of electron
Bohr's second postulate (the quantisation condition) allows the electron only those orbits in which its angular momentum is an integral multiple of \( h/2\pi \):
\( \displaystyle mvr = \frac{nh}{2\pi}, \quad n = 1, 2, 3, \ldots \)
The other quantities are quantised too, but not as multiples of \( h/2\pi \): the radius varies as \( n^{2} \), and the kinetic and potential energies vary as \( 1/n^{2} \). Also, \( h/2\pi \) has the unit J s, which is the unit of angular momentum and not of energy or length.
NCERT (2026-27):
Bohr Model of the Hydrogen 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
\( \displaystyle L = nh/2\pi \qquad (12.5) \)”