Question

Statement A: Density of nucleus is independent of its mass number
Statement B: Beryllium is used as a moderator in nuclear reactors
A. Both A and B are correct
B. Both A and B are wrong
C. A is correct, B is wrong
D. A is wrong, B is correct

Answer 1

Hint: The radius of a nucleus depends on the cube root of radius and we can calculate volume of the nucleus from radius and density is equal to mass per unit volume. An element which can efficiently absorb energy of neutrons is used as moderator in nuclear reactors.

Complete step-by-step answer:
Consider statement A: Density of nucleus is independent of its mass number
We know that the radius of a nucleus depends on the mass number of the nucleus through the following relation.
$R = {R_0}{A^{\dfrac{1}{3}}}$
The density of a nucleus is equal to mass number divided by the volume of the nucleus. Volume of the nucleus $= \dfrac{4}{3}\pi {R^3}$. Therefore, we have
$\rho = \dfrac{A}{{\dfrac{4}{3}\pi {R^3}}}$
Inserting the value of R, we get
$\rho = \dfrac{A}{{\dfrac{4}{3}\pi R_0^3{{\left( {{A^{\dfrac{1}{3}}}} \right)}^3}}} \\\ = \dfrac{A}{{\dfrac{4}{3}\pi R_0^3A}} = \dfrac{3}{{4\pi R_0^3}} \\\$
It is clear that the density of the nucleus does not depend on the mass number A of the nucleus. Therefore, statement A is correct.

Consider statement 2: Beryllium is used as a moderator in nuclear reactors
In a nuclear reaction, large numbers of neutrons are produced which have high kinetic energy. In order to continue the chain reaction, we need slow moving neutrons and a moderator slows down these neutrons by absorbing their energy and beryllium has very good absorbing power so it is used as a moderator. Therefore statement 2 is also correct.
The correct answer is option A.

Note: 1. All nuclei have the same density irrespective of their mass number i.e. the number of nucleons (protons + neutrons).
2. The fast moving electrons undergo inelastic scattering with the moderator transferring their kinetic energy during the process.