Home / Topics / Atomic & Nuclear Physics
Nuclear size
Intermediate
Radius scales as cube root of A.
Key relation
R = R₀A^{1/3}R = R₀A^{1/3} with R₀ ≈ 1.2 fm. Volume ∝ A, so all nuclei have about the same density.
Worked example
Uranium-238: 7.4 fm.
Common mistake
Size is a rough, fuzzy boundary.
In more detail
Nuclear size scales with the cube root of the mass number, R = R0 A^(1/3), with R0 about 1.2 femtometres. Nuclei are roughly spherical and very small compared with atoms.
Real-world uses
- Scattering experiments measure nuclear sizes.
- Nuclear models use the size relation for calculations.
- Nuclear physicists estimate the size of a nucleus from scattering experiments, which show that it grows with the cube root of mass number.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
How small is a femtometre?
One quadrillionth of a metre.
Why does size scale with A^(1/3)?
Because nuclear matter has roughly constant density.
Why does the radius scale as the cube root?
The nucleus has nearly constant density, so its volume is proportional to the number of nucleons.
Related topics in Atomic & Nuclear Physics
Atomic mass unit · Nucleus composition · Isotopes, isobars, isotones · Nuclear density · Mass defect · Binding energy