Ncert Exercises & Solutions

13.21 From the relation R = R₀A^1/3, where R₀ is a constant and A is the mass number of a nucleus, show that the nuclear matter density is nearly constant (i.e. independent of A).

Hint: Nuclear density does not depend on the value of mass number.
Step 1: Write the formula of nuclear density.
We have the expression for nuclear radius as:

R = R_{0} A^{1} /^{3}

where,

R_{0}

=Constant

A=Mass number of the nucleus.

Nuclear matter density,

ρ = \frac{M a s s o f t h e n u c l e u s}{V o l u m e o f t h e n u c l e u s}

Step 2: Find the nuclear density.
Let m be the average mass of the nucleon. Hence, mass of the nuleus=mA

∴ ρ = \frac{m A}{\frac{4}{3} π R^{3}} = \frac{3 m A}{4 π {(R_{0} A^{\frac{1}{3}})}^{3}} = \frac{3 m A}{4 π R_{0}^{3} A} = \frac{3 m}{4 π R_{0}^{3}}

Hence, the nuclear matter density is independent of A. It is nearly constant.

NEET Information

courses

Company

Botany Questions

Chemistry Questions

Physics Questions

Zoology Questions