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Question

In the study of Geiger-Marsdon experiment on scattering of αparticles by a this foil of gold, draw the trajectory of αparticles in the coulomb field of target nucleus. Explain briefly how one gets the information on the size of the nucleus from this study:
From the relation R=R0A1/3, where R0 is constant and A is the mass number of the nucleus, show that nuclear matter density is independently of A

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Solution

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=43πR3
V=43π(RoA1/3)3
V=43πR3oA
Density of the nucleus is ρ=MV
ρ=mA43πR3oA
ρ=3m4πR3o
Hence, nuclear density is independent of A.

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