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Question

As the mass number A increases, which of the following quantities related to a nucleus do not change?
(a) Mass
(b) Volume
(c) Density
(d) Binding energy

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Solution

(c) Density

Radius of a nucleus with mass number A is given as
R=RoA13
Here, Ro = 1.2 fm
∴ Volume of the nucleus = 4πR33=4πRo3A3

This depends on A. With an increase in A, V increases proportionally.
Mass of the nucleus AmN
Here, mN is the mass of a nucleon.
Therefore, mass of the nucleus also increases with the increasing mass number.
Binding energy also depends on mass number (number of nucleons) as it is the difference between the total mass of the constituent nucleons and the nucleus. Therefore, it also varies with the changing mass number.

On the other hand,
Density = MassVolume=AmN4πR33=AmN4πRo3A3=mN4πRo33=3mN4πRo3
This is independent of A and hence does not change as mass number increases.

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