If we make a simple assumption, that each nucleon in the nucleus occupies a fixed volume, with no space between the nucleons (a very big assumption), then the volume of the nucleus will be proportional to the number of nucleons.
If we further assume the nucleus to be as nearly spherical as possible, it will have volume
The volume we have assumed to be proportional to the number of nucleons, or the Mass number
so that
so that
Making
the subject of this equation gives
where
Some experimental values are given below alongside theoretical values using the above equation.
|
Element |
Isotope Mass |
Experimental Radius, m |
Theoretical Radius, m |
|
Carbon - 12 |
12 |
|
|
|
Silicon - 28 |
28 |
|
|
|
Iron - 56 |
56 |
|
|
|
Tin -120 |
120 |
|
|
|
Lead - 208 |
208 |
|
|
Agreement is to within just over 10%.