Which of the following statements are correct?
A. The various lines in the atomic spectra are produced when electrons jump from higher energy state to a lower energy state.
B. An accelerated atomic electron must spiral into the nucleus as it loses energy.
C. Rutherford scattering determines an upper limit to the size of the nucleus.
D. Angular momentum of the electron orbiting around the nucleus is not quantised.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → A, B and C Only
The statements test the Rutherford model, its classical difficulty, and Bohr's postulates.
A. The various lines in the atomic spectra are produced when electrons jump from higher energy state to a lower energy state. — Correct. In an emission spectrum, each line is a photon of energy \( h\nu = E_i - E_f \) given out when the electron jumps down from a higher level to a lower one.
B. An accelerated atomic electron must spiral into the nucleus as it loses energy. — Correct. By classical electromagnetic theory, an electron moving in a circle is accelerated and so radiates energy; its orbit would shrink and it would spiral into the nucleus. This failure of the Rutherford model led to Bohr's postulates.
C. Rutherford scattering determines an upper limit to the size of the nucleus. — Correct. The distance of closest approach of the alpha particles in a head-on collision is about \( 10^{-14}\,\mathrm{m} \); the nucleus must be smaller than this, so the experiment gives an upper limit to its size.
D. Angular momentum of the electron orbiting around the nucleus is not quantised. — Incorrect. By Bohr's second postulate the angular momentum is quantised, \( L = n h/2\pi \).
NCERT (2026-27):
The Line Spectra of the Hydrogen Atom – “… The various lines in the atomic spectra are produced when electrons jump from higher energy state to a lower energy state and photons are emitted.”
Summary – “… 4. Rutherford nuclear model has two main difficulties in explaining the structure of atom: (a) It predicts that atoms are unstable because the accelerated electrons revolving around the nucleus must spiral into the nucleus.”
Alpha-Particle Trajectory – “… Rutherford scattering therefore, is a powerful way to determine an upper limit to the size of the nucleus.”
De Broglie’s Explanation of Bohr’s Second Postulate of Quantisation – “… It states that the angular momentum of the electron orbiting around the nucleus is quantised.”