Class 12 Physics Nuclei Size of Nucleus

Size of Nucleus

• Rutherfordperformed an experiment which proved that the size of the nucleus is extremely small.
• In Rutherford scattering experiment a beam of alpha particles were made to pass through a small thin gold foil.
• Very few alpha particles were deflected.
• The alpha particles got deflected because of repulsion with the nucleus as alpha particles are positively charged.They get repelled because they are both positively charged.
• Very small number of alpha particles got deflected provingthat nucleus is very small in size.
• It was found that the radius of a nucleus(R) of mass number A is given as :-
• R=R0A1/3 where A = mass number and R0=constant.
• Volume of a nucleus is ∝to the mass number.
• V =(4/3)πR3 , Also R ∝(A)1/3
• => (R)3∝A
• Therefore V (R) 3
• Density of nucleus is independent of mass number.

Problem:- Given the mass of iron nucleus as 55.85u and A=56,find the nuclear density?

Answer:- Given: - mFe = 55.85, u = 9.27 × 10–26 kg

Nuclear density =mass/volume

= (9.27 × 10–26)/((4 π /3)(1.2x 10-15)3)x (1/56)

= 2.29 × 1017 kg m–3

The density of matter in neutron stars (an astrophysical object) iscomparable to this density. This shows that matter in these objectshas been compressed to such an extent that they resemble a bignucleus.

Rutherford’s Gold Foil Experiment  .