(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)
S safeer

(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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