Which one of the following could not be explained by Rutherford's nuclear model?

Correct — A, Stability of the atom. Rutherford's model has an electron moving in an orbit around the nucleus, and that is where it breaks. An electron travelling on a curved path is accelerating, because its direction is constantly changing, and classical electromagnetic theory says that an accelerating charge must radiate energy. An orbiting electron would therefore lose energy continuously, spiral inward, and fall into the nucleus — on the classical estimate in something of the order of a hundred-millionth of a second. Atoms plainly do not do this. The model also predicts that the frequency of the radiation would change smoothly as the orbit shrank, giving a continuous spectrum, whereas atoms actually emit sharp, discrete spectral lines. Both failures have the same root, and both were the problem Bohr's model of 1913 was built to solve, by postulating that electrons occupy only certain permitted orbits in which they do not radiate. The other three options are not failures at all — they are precisely what the scattering experiment established and what the model was constructed to express.

• (b)Presence of nucleus in the centre of an atom — This is the model's central success, not a failure. Large-angle scattering of alpha particles is exactly what led Rutherford to place a nucleus at the centre.
• (c)Comparison of sizes of atom and nucleus — Also accounted for. Because almost all the alpha particles passed straight through the foil, the nucleus had to be minute compared with the atom — the model gives that ratio, of the order of one to ten thousand.
• (d)Nucleus is positively charged — Another success. Alpha particles are positively charged, and only a positive centre would repel them strongly enough to turn them through large angles.

Rutherford's nuclear model, of 1911, places nearly all the atom's mass and all its positive charge in a tiny central nucleus, with electrons in the surrounding space. It explained the scattering results completely. What it could not do was survive its own mechanics: classical physics forbids a stable orbiting electron. Bohr's model resolved this by quantisation — electrons occupy only certain allowed orbits of fixed energy, radiate nothing while in them, and emit or absorb a photon only when jumping between them, which also accounts for discrete spectral lines.

This question and question 56 of the same paper are the two halves of one topic, and the paper is testing whether a candidate can hold them apart. Question 56 asks what the experiment discovered; this one asks what the resulting model could not explain. A clean way to keep the distinction is to separate observation from mechanics. Everything the experiment observed — where the mass is, where the charge is, how small the nucleus is — the model handles. Everything about how the electron then behaves over time, the model cannot. So when an option describes something about the atom's structure, it is a success; when it describes the atom persisting or emitting light, it is a failure. Note in passing that Rutherford's model is sometimes described as failing to explain the atom's spectrum as well; that is the same defect seen from another angle, and either phrasing points to the same answer.

• Rutherford proposed the nuclear model in 1911, following the alpha-particle scattering results.
• An electron in a curved orbit is accelerating, and classical electromagnetism requires an accelerating charge to radiate energy.
• A radiating electron would spiral into the nucleus in a very short time, so the model cannot account for atomic stability.
• The model also predicts a continuous spectrum, whereas atoms emit sharp discrete spectral lines.
• Bohr's model of 1913 fixed both defects by postulating stationary orbits in which the electron does not radiate.
• The model's successes — a central, positively charged nucleus, minute compared with the atom — all follow directly from the scattering data.

• Reading the question as 'what did the experiment fail to show' rather than 'what did the model fail to explain'.
• Picking a structural feature — nucleus, charge, size — when all three are the model's successes.
• Forgetting that the discrete-spectrum failure and the stability failure are the same defect described two ways.

Extremely common, usually worded exactly as here. The companion question — what the experiment discovered — appears in this same paper at question 56.

• practice — not a real PYQ

  According to classical electromagnetic theory, an electron revolving around the nucleus should

  • (a)remain in a fixed orbit indefinitely
  • (b)continuously radiate energy and spiral into the nucleus
  • (c)gain energy from the nucleus
  • (d)emit radiation only when struck by a photon

  Answer(b) continuously radiate energy and spiral into the nucleus — the accelerating charge must radiate, which is precisely why the nuclear model cannot explain atomic stability.

• practice — not a real PYQ

  The defect of Rutherford's model regarding atomic stability was addressed by

  • (a)J. J. Thomson
  • (b)Niels Bohr
  • (c)James Chadwick
  • (d)John Dalton

  Answer(b) Niels Bohr — his 1913 model postulated stationary orbits in which the electron does not radiate.