In the study of the Geiger-Marsdon experiment on scattering of α-particles by a thin gold foil, draw the trajectory of α-particles in the Coulomb field of the target nucleus. Explain briefly how one gets the information on the size of the nucleus from this study. From the relation R = R₀A^(1/3), where R₀ is a constant and A is the mass number of the nucleus, show that nuclear matter density is independent of A.

The trajectory of α- particles in the gold foil experiment is shown in the attached figure. As most of the particles are undeflected, this suggests that the nucleus occupies only a small volume of the total atom.

Let m be the mass of the nucleon and R be the radius of the nucleus.
Mass of the nucleus is M = mA
Volume of the nucleus is V = (4/3)πR³
V = (4/3)π(R₀A^(1/3))³
V = (4/3)πR₀³A
Density of the nucleus is ρ = M/V
ρ = mA/((4/3)πR₀³A)
ρ = 3m/(4πR₀³)

Hence, nuclear density is independent of A.