Rutherford's Experiment - Size of the Nucleus


Understanding the fundamental structure of matter is essential to Physics. Figuring out the size of the nucleus which is the crux of this article would not be possible without the Rutherford gold foil experiment. The Rutherford model of the atom was the first correct interpretation of the atom and it laid the groundwork for Bohr to build his interpretation on.

Rutherford Gold Foil Experiment

Before Rutherford’s experiment, the best model of the atom that was known to us was the Thomson or “plum pudding” model. In this model, the atom was believed to consist of a positive material “pudding” with negative “plums” distributed throughout. Later, Rutherford’s alpha-particle scattering experiment changed the way we think of the atomic structure. Rutherford directed beams of alpha particles at thin gold foil to test this model and noted how the alpha particles scattered from the foil.

JJ Thompson Plum Pudding Model

Rutherford in the gold foil experiment showed us that the atom was mainly empty space with the nucleus at the centre and electrons revolving around it. When he fired alpha particles towards the gold foil, he noticed that 1 in 20000 particles suffered a change in direction of motion of more than 90 degrees. Rest of the 19999 article departed from their trajectory by a very small margin. This meant that the atom consisted of an empty space with most of the mass being concentrated in tiny volume in the centre. He called this volume ‘the nucleus’; Latin for ‘little nut’.

Rutherford Gold Foil Experiment

Through this experiment, Rutherford made 3 observations as follows:

  • Highly charged alpha particles went straight through the foil undeflected. This would have been the expected result for all of the particles if the plum pudding model was correct.
  • Some alpha particles were deflected back through large angles.
  • A very small number of alpha particles were deflected backwards! To this Rutherford remarked, “It was as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back at you!”

To explain these observations, a new model of the atom was needed. In the new model, the positive material was considered to be concentrated in a small but massive region called the nucleus. Electrons were considered to be revolving around the nucleus preventing one atom from trespassing on its neighbour’s space to complete this model.

Size of Nucleus

Through the Rutherford experiment, it was possible to obtain the size of the nucleus. By obtaining the point of closest approach of an alpha particle, we could calculate the size of the nucleus. By firing alpha particles of kinetic energy 5.5 MeV, the point of closest approach was calculated to be about 4×10-14m. Since the repulsive force acting here is Coulomb repulsion, there is no contact. This means that the size of the nucleus is smaller than 4×10-14m.

By firing alpha particles of greater energy and after many more iterations of the experiment, the sizes of the nuclei of various elements have been accurately measured. Through this, we have obtained a formula to measure the size of the nucleus.

\(R\) =\( R_0 A^{\frac{1}{3}}\)

Where R0 = 1.2×10-15m. This means that the volume of the nucleus which is proportional to R3 is proportional to A (mass number). One thing that should also be noticed is that there seems to be no mention of density in the equation. That’s because the density of the nuclei does not vary with elements. All nuclei have the same density. The density of the nucleus is approximately 2.3×1017 kg.m-3. This is very high compared to the density of normal things, ie water (1000 kg.m-3) or air (1.225 kg.m-3). This is because most of the atom is empty and all the mass is concentrated in a very tiny space.

Frequently Asked Questions

  1. What did RutherFord’s gold foil experiment teach us about the atomic structure?
  2. Rutherford’s gold foil experiment showed us that the atom is mostly empty space with a comparatively tiny, massive, positively charged nucleus in the centre.

  3. What caused the alpha particles to deflect in Rutherford’s gold-foil experiment?
  4. Rutherford thought that the particles would fly straight through the foil. However, he found that the path of the particle would be shifted or deflected when passing through the foil. This is due to the fact that like charges repel each other.

  5. How did Rutherford’s experiment affect our world?
  6. Rutherford’s experiment provided us with a better, more practical understanding of matter. The experiment provided conclusive evidence against previous conceptions of matter and provided a new model consistent with the facts.

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