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.
Consider the following statements:
(A) On a stretched string, standing waves are formed when the total distance travelled by a wave down the string and back is a whole number of wavelengths.
(B) De Broglie gave his explanation of Bohr’s second postulate in 1923, about ten years after Bohr proposed his model.
(C) Bohr’s model correctly explains the relative intensities of the lines in the hydrogen spectrum.
(D) Bohr’s model takes into account the electric forces between the electrons of an atom.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A) and (B) only
De Broglie used the standing waves on a string to explain the allowed orbits. Bohr’s model itself still has some limits.
(A) On a stretched string, standing waves are formed when the total distance travelled by a wave down the string and back is a whole number of wavelengths. — True. Waves of other wavelengths interfere with themselves after reflection and soon die out. Only a whole number of wavelengths over the trip down and back survives.
(B) De Broglie gave his explanation of Bohr’s second postulate in 1923, about ten years after Bohr proposed his model. — True. Bohr gave his model in 1913. De Broglie explained the second postulate in 1923.
(C) Bohr’s model correctly explains the relative intensities of the lines in the hydrogen spectrum. — False. The model gives the frequencies of the lines correctly. It cannot explain why some lines are strong and others weak.
(D) Bohr’s model takes into account the electric forces between the electrons of an atom. — False. The model uses only the electric force between the nucleus and the electron. It leaves out the forces between electrons, so it fails for atoms with two or more electrons.
NCERT (2026-27):
De Broglie’s Explanation of Bohr’s Second Postulate of Quantisation – “… It means that in a string, standing waves are formed when the total distance travelled by a wave down the string and back is one wavelength, two wavelengths, or any integral number of wavelengths. …”
De Broglie’s Explanation of Bohr’s Second Postulate of Quantisation – “… The French physicist Louis de Broglie explained this puzzle in 1923, ten years after Bohr proposed his model.”
De Broglie’s Explanation of Bohr’s Second Postulate of Quantisation – “(ii) While the Bohr’s model correctly predicts the frequencies of the light emitted by hydrogenic atoms, the model is unable to explain the relative intensities of the frequencies in the spectrum. …”
De Broglie’s Explanation of Bohr’s Second Postulate of Quantisation – “The formulation of Bohr model involves electrical force between positively charged nucleus and electron. It does not include the electrical forces between electrons which necessarily appear in multi-electron atoms.”