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.
In de Broglie’s explanation, the momentum of the orbiting electron is taken as \(mv_n\), where \(v_n\) is its speed in the \(n\)th orbit. This is valid when
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → its speed is much less than the speed of light
Option (1) its speed is much less than the speed of light — Correct. For a speed much less than the speed of light, the momentum is \( mv_n \). So the de Broglie wavelength becomes \( \lambda=h/mv_n \).
Option (2) it is in the ground state — Incorrect. The same form is used for every orbit, \( n=1,2,3\ldots \). It leads to Bohr’s condition for all of them.
Option (3) the quantum number \(n\) is very large — Incorrect. It holds for small \( n \) too. The condition is on the speed of the electron, whatever the value of \( n \).
Option (4) its orbit is a circle — Incorrect. The shape of the path does not decide the form of the momentum. Only the speed compared with the speed of light does.
NCERT (2026-27):
De Broglie’s Explanation of Bohr’s Second Postulate of Quantisation – “… If the speed of the electron is much less than the speed of light, the momentum is mvn. Thus, λ = h/ mvn. …”