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Nuclear radius

The scattering of high energy electrons by nucleons (protons and neutrons) can reveal the internal structure of these particles.

Fermi proposed the equation for the radius of a nucleus (r) in terms of the radius of the hydrogen nucleus (r_o) and the nucleon number of the nucleus (A)

Fermi equation for nuclear radius: r = r_oA^1/3

The constant r_o = 1x10^-15 m = 1 Fm

Example problem
Calculate the radii of the following nuclei:
(a) carbon 12 (A = 12)
(b) gold 197 (A = 197)

(a) r = 10^-15x12^1/3 = 2.3x10^-15 m = 2.3 Fm
(b) r = 10^-15x197^1/3 = 5.8x10^-15 m = 5.8 Fm

From the Fermi equation (r = r_oA^1/3) we know that the "diameter" of a nucleon is about 10^-15 m and so if we want to have any chance of "seeing" inside a proton we need to use something with a wavelength of this order or even smaller.

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