3.8.1.5
Nuclear radius depends on mass number: $R = R_{0}A^{1/3}$
Nuclear Structure & Radiation — AQA A-Level Physics
- Nuclear radii are of the order 10⁻¹⁵ m (1 $fm = 1 femtometre)$.
- As more nucleons are added, the nucleus gets bigger, but R is not proportional to A.
$$R = R_0 A^{1/3}$$
- $R$: nuclear radius (m)
- $R₀$: constant of proportionality ≈ 1.05 fm
- $A$: nucleon (mass) number
- A graph of R against \(A^{1/3}\) gives a straight line through the origin with gradient R₀.
- Taking logarithms: ln $R = (1/3) \ln A + \ln R_{0}. A graph$ of ln R against ln A gives gradient 1/3 and y-intercept ln R₀.
- Example values: Carbon (A=12) R = 2.66 fm, Iron (A=56) R = 4.35 fm, Lead ($A=208) R = 6.66 fm$.