← Nuclear Physics

# Nuclear Sizes and Shapes

Friday, April 1, 2022

## Atomic Density

The density of a nucleus is fairly constant (it does not increase in density drastically towards the center). Additionally, the density at the center of the nucleus is not correlated with mass number $A$; atoms tend to have approximately the same density:

$\frac{\text{number of neutrons and protons}}{\text{volume of nucleus}}=\frac{A}{\frac{4}{3}\pi R^3}\approxeq \text{constant}$

Assuming the nucleus is a sphere of radius $R$, the constant of proportionality $R_0$ is therefore defined as

$R=R_0A^{1/3}$

Experimentally, this value is found to be approximately $1.2\times 10^{-15}~\text{m}$.

## Rutherford Scattering

The size of the nucleus can be measured using Rutherford scattering, where alpha particles are sent into atoms. If the alpha particle is outside the nucleus, the Rutherford scattering formula is relatively accurate, however, it begins to deviate when the closest approach is less than the nuclear radius.