# 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

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’.

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.