Physics · Atoms and nuclei · chapter 12 of 14

Class 12 Physics Chapter 12: Atoms case study question with answers

One case-based question of the kind the board asks: a passage, then 3 parts worth 4 marks in all, with the answer and the marking scheme for each. Written from the NCERT chapter.

Case study · 4 marks
A student repeats the essentials of the Geiger–Marsden experiment in a simulation. A beam of α-particles, each of kinetic energy 5.0 MeV, falls on a very thin foil of silver (Z = 47). The simulation treats each α-particle as being scattered by at most one nucleus, and holds the silver nucleus fixed during the encounter, since it is many times heavier than the α-particle. It reports that nearly all the α-particles pass with little or no deflection, while a very small number are turned back, and that an α-particle aimed head-on comes momentarily to rest 27 fm from the centre of the nucleus before reversing.
Part 1 · 1 mark
The very small number of α-particles turned back shows that
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Answer: (b) the positive charge and most of the mass of the atom are concentrated in a very small volume

Few rebounds mean few head-on collisions, which means the mass and positive charge sit in a very small volume. A uniform spread could not reverse any α-particle.

Part 2 · 1 mark
If the kinetic energy of the α-particles is raised to 7.5 MeV, the distance of closest approach in a head-on encounter becomes
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Answer: (d) 18 fm

d = 2Ze²/(4πε₀K) ∝ 1/K, so d = 27 × 5.0/7.5 = 18 fm. 40.5 fm takes d ∝ K; 12 fm takes d ∝ 1/K²; 22 fm takes d ∝ 1/√K.

Part 3 · 2 marks
Why is it reasonable to treat each α-particle as scattered by at most one nucleus, and why do the electrons of the silver atoms play no appreciable part in the scattering?
Answer and marking scheme

The foil is very thin and the atom is mostly empty space with a tiny nucleus, so an α-particle is unlikely to pass close to more than one nucleus; one trajectory per nucleus is enough. The electrons are very light compared with the α-particle, so they cannot deflect it appreciably.

  • thin foil, mostly empty atoms: at most one close encounter (1)
  • electrons too light to deflect the α-particle (1)
Or
Explain why a measured distance of closest approach gives only an upper limit to the size of the nucleus.
Answer and marking scheme

The α-particle reverses at distance d because the electric repulsion stops it, while it is still outside the nucleus; it never touches the nucleus. So the nucleus must be smaller than d, and d is only an upper limit to its radius (for gold, d ≈ 30 fm while the actual radius is about 6 fm).

  • α-particle stops outside the nucleus without touching it (1)
  • so radius < d; d is an upper limit (1)
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