(a) Explanation of information on the size of nucleus
(b) Showing the independence of density on mass number
(a) Many of the α-particles pass through the foil. A few particles deflect by more than 90∘.
Rutherford argued that to deflect the α-particles backward, it must experience a large repulsive force.
It shows that most of the part of an atom is the empty space and its positive charge is concentrated tightly at its centre and its size is very small as compared to the size of atom.
(nearly ‌

1

10,000

to ‌

1

10,000

times the size of atom)
Alternatively,
In Rutherford experiment, the calculation of distance of closest approach provides information about the size of the nucleus.
Let K be the initial kinetic energy of the alpha particle.
At the distance of closest approach
‌‌

1

4πε0

‌

(Ze)(2e)

a2

=k
‌∴‌‌a=‌

2Ze2

4πε0k

(b) Radius of the nucleus of mass number A, R=R0A1∕3, where, R0 is constant.
Volume of the nucleus,
V‌=‌

4

3

πR3
‌=‌

4

3

π(R0A1∕3)3
‌=‌

4

3

πAR0‌3
Density(ρ)‌=‌

‌ mass ‌

‌ volume ‌

=‌

mA

(‌ 4 3 πR0‌3A)

‌=‌

3m

4πR0‌3

i.e., independent of mass number A.