Physics · Atoms · NEET
Three things. (1) Most alpha-particles passed straight through, so the atom is mostly empty space. (2) A few bent by large angles, so there is a strong repulsive charge concentrated in a very small region. (3) About 1 in 8000 bounced back by more than 90 degrees, so nearly all the mass and all the positive charge sit in a tiny centre called the nucleus. Electrons revolve around this nucleus at a large distance.
Gold is very malleable, so it can be beaten into an extremely thin foil (about 2.1 x 10^-7 m thick, only a few hundred atoms thick). A thin foil means each alpha-particle usually meets only ONE nucleus. If the foil were thick, particles would scatter many times and the single-scattering pattern would be lost. Gold also has a high atomic number (Z = 79), giving a strong nuclear charge and clear large-angle scattering.
The few particles that made an almost head-on approach (very small impact parameter) rebounded back by nearly 180 degrees. This was the surprising result. Rutherford said it was as unlikely as a shell bouncing off tissue paper. To turn a fast alpha-particle around, there must be a very large repulsive force, which is only possible if all the positive charge and mass are packed into a tiny, hard nucleus.
At the closest point the alpha-particle stops for an instant, so all its kinetic energy has become electric potential energy: (1/2)mv^2 = (1/4 pi e0)(2Ze^2)/r0. Solving gives r0 = (1/4 pi e0)(4Ze^2)/(mv^2). So for fixed speed, r0 is proportional to 1/m, and for fixed mass, r0 is proportional to 1/v^2. Faster or heavier particles get closer to the nucleus.
No. The NCERT calculation for a 7.7 MeV alpha-particle gives a distance of closest approach of about 30 fm (3.0 x 10^-14 m), but the real radius of a gold nucleus is only about 6 fm. So the alpha-particle stops and reverses well before reaching the nuclear surface. The experiment gives only an UPPER LIMIT for the size of the nucleus, not its exact radius.
The number of scattered particles N is huge at small angles and falls off very steeply as the angle grows, following N proportional to 1/sin^4(theta/2). Most particles scatter by tiny angles; only a very small number reach large angles. The curve is NOT a peak at 90 degrees and NOT flat, it drops sharply from small angles.
When an alpha-particle of mass m moving with velocity v bombards a heavy nucleus of charge Ze, its distance of closest approach from the nucleus depends on m as:
In the Geiger-Marsden experiment, the number of scattered alpha-particles N(theta) is plotted as a function of scattering angle theta. Which option represents the correct plot?
Try the real previous-year questions from this chapter — each with the answer and a full solution.
H. Geiger and E. Marsden performed the experiments in 1911, at the suggestion of Ernst Rutherford. Rutherford interpreted the results and proposed the nuclear model, so it is often called the Rutherford (Geiger-Marsden) experiment.
A radioactive source of Bismuth-214 (Bi-214). The alpha-particles were collimated into a narrow beam using lead bricks before hitting the gold foil.
By a rotatable zinc sulphide (ZnS) screen with a microscope. Each alpha-particle striking the screen made a tiny flash of light (a scintillation), which was counted at different angles.
About 0.14 percent of the incident alpha-particles scattered by more than 1 degree, and only about 1 in 8000 deflected by more than 90 degrees. These rare large-angle events revealed the tiny nucleus.
Rutherford estimated the nucleus to be about 10^-15 to 10^-14 m, while the atom is about 10^-10 m. The atom is roughly 10,000 to 100,000 times larger than its nucleus, so it is mostly empty space.
The impact parameter b is the perpendicular distance of the alpha-particle's initial velocity line from the centre of the nucleus. Small b (near head-on) gives large scattering; large b gives almost no deflection.
