Which of the following is NOT true for Bohr’s model of the hydrogen a…

The correct answer is Option (1) → The electron can revolve in any orbit around the nucleus without emitting radiant energy.

Option (1) The electron can revolve in any orbit around the nucleus without emitting radiant energy. — Not true for Bohr’s model. By Bohr’s first postulate the electron revolves without radiating only in certain stable orbits, the stationary states. The second postulate picks out these orbits as the ones with \( L=nh/2\pi \). No other orbit is allowed.

Option (2) The angular momentum of the electron is directly proportional to the orbit number \( n \). — True for Bohr’s model. Since \( L=nh/2\pi \) and \( h/2\pi \) is a constant, \( L \) is proportional to \( n \).

Option (3) The angular momentum of the electron is an integral multiple of \( h/2\pi \). — True for Bohr’s model. This is the quantisation condition of the second postulate, \( L=nh/2\pi \) with \( n=1,2,3,\ldots \).

Option (4) The radius of the orbit is proportional to the square of the principal quantum number \( n \). — True for Bohr’s model. The radius of the nth orbit is \( r_n=n^2a_0 \), where \( a_0 \) is the Bohr radius, so \( r_n\propto n^2 \).

NCERT (2026-27):
Bohr Model of the Hydrogen Atom – “(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.”

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/2π where h is the Planck’s constant (= 6.6 × 10^–34 J s).”