(a) Explain briefly how Rutherford scattering of \alpha-particle by a target nucleus can provide information on the size of the nucleus.
(b) Show that the density of the nucleus is independent of its mass number A.

 

 
 
 
 
 

Answers (1)

(a) In the rutherford famous gold fail experiment most of the \alpha - particle pass through the tail undeflected signifying that most of the space inside an atom is empty and many of them get deflected by a very small angle implying that the nature of the charge in the atom (nucleus), located at the centre should be same as the \alpha - particles. i.e positive. out of 8,000 \alpha - particle, one of them gets deflected for almost 180^{o}, signifies that very dense is situated at the centre of the atom.

(b) Let us consider the volume of the nucleus be V and the mass of nucleons be m.

We also know, r=r_{o}A^{1/3} where r_{o} lies between 1.2 fermi to 1.5 fermi,

Density

\rho=\frac{mass}{volume}

\rho=\frac{mA}{\frac{4}{3}\pi r_0^3A}=\frac{3m}{4\pi r_0^3}

The above equation implies that the density of the nucleus is independent of its mass number

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