Read the following passage and answer the questions.
In Bohr’s model of the hydrogen atom, the electron moves only in certain allowed orbits. Bohr’s second postulate picks out these orbits. Of all his postulates, it looked the most puzzling, because it gave no reason for this choice. The French physicist Louis de Broglie later gave a reason. He had suggested that material particles, such as electrons, also have a wave nature. He argued that the electron in its circular orbit must be seen as a particle wave. Waves travelling on a stretched string can form standing waves when the conditions are right. In the same way, the particle wave of the electron can form a standing wave along its orbit. This idea explains why only certain orbits are allowed. It links the allowed orbits of the atom to the wave nature of the electron.
Match List-I with List-II.
| List-I | List-II |
|---|---|
| (A) Bohr’s first postulate | (I) A photon is emitted with energy equal to the energy difference between the initial and final states. |
| (B) Bohr’s second postulate | (II) A nucleus of charge \(+Ze\) with a single electron |
| (C) Bohr’s third postulate | (III) An electron revolves in certain stable orbits without emitting radiant energy. |
| (D) Hydrogenic atom | (IV) The angular momentum of the electron is an integral multiple of \(h/2\pi\). |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A)-(III), (B)-(IV), (C)-(I), (D)-(II)
(A) Bohr’s first postulate — This matches (III). It says the atom has stationary states. In these, the electron moves in a stable orbit and does not radiate.
(B) Bohr’s second postulate — This matches (IV). It picks out the allowed orbits by the condition \( L=nh/2\pi \).
(C) Bohr’s third postulate — This matches (I). When the electron jumps to a lower orbit, the energy lost leaves as one photon, with \( h\nu=E_i-E_f \).
(D) Hydrogenic atom — This matches (II). Hydrogen, singly ionised helium and doubly ionised lithium each have one electron around a nucleus of charge \( +Ze \).
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. …”
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 …”
Bohr Model of the Hydrogen Atom – “(iii) Bohr’s third postulate … 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. …”
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. …”