Answer

Verified

439.8k+ views

**Hint:**To show that nuclear matter density is independent of A, we need to find nuclear matter density. Nuclear matter density is the density of an atom’s nucleus. To find the density, we substitute the values of mass and volume of the nucleus in the equation for density.

**Formula used:**

Density,$\rho $ is given by

$\rho =\dfrac{M}{V}$

**Complete step by step answer:**

The trajectory of the α-particle in the coulomb field is given below.

In the α-particles scattering experiment, most of the particles remained undeflected. Only a very small fraction of the particles deflected back. The α-particles are having positive charge and are deflected by the positive charge of the nucleus. So we can conclude that the nucleus occupies only a small volume of the total atom.

Let us assume that m is the mass of the nucleon and R is the radius of the nucleus. It is given that A is the mass number of the nucleus. So, the mass of the nucleus is given by,

$M=mA$

We assume that the nucleus is a sphere and the volume of the nucleus is given by,

$V=\dfrac{4}{3}\pi {{R}^{3}}$

It is given that $R={{R}_{0}}{{A}^{\dfrac{1}{3}}}$

$\Rightarrow V=\dfrac{4}{3}\pi {{\left( {{R}_{0}}{{A}^{\dfrac{1}{3}}} \right)}^{3}}$

On simplification, we get,

$V=\dfrac{4}{3}\pi {{R}_{0}}^{3}A$

Density of a material is defined as mass per unit volume. The density of the nucleus is given by,

$\rho =\dfrac{M}{V}$

Substituting the values of M and V, we get,

$\rho =\dfrac{mA}{\dfrac{4}{3}\pi {{R}_{0}}^{3}A}$

On simplification, we get,

$\rho =\dfrac{3m}{4\pi {{R}_{0}}^{3}}$

Thus nuclear matter density is independent of A.

**Note:**

The Geiger-Marsden experiment was done between the years 1908-1913 by Rutherford and his assistants Geiger and Marsden. This experiment gave the proof that JJ Thomson’s plum pudding model of atom and nuclei was a wrong conclusion.

Recently Updated Pages

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Advantages and disadvantages of science

Trending doubts

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Difference Between Plant Cell and Animal Cell

Which are the Top 10 Largest Countries of the World?

10 examples of evaporation in daily life with explanations

Give 10 examples for herbs , shrubs , climbers , creepers

Write a letter to the principal requesting him to grant class 10 english CBSE

Change the following sentences into negative and interrogative class 10 english CBSE