The volume of a nucleus is directly proportional to _______

(Where A = mass number of the nucleus)

The correct answer is option 4) i.e. A.

CONCEPT:

• Nucleus: The nucleus is a small dense region at the center of an atom, containing protons and neutrons.
  • The mass of an atom is located in the nucleus, with a very small contribution from the electrons.

The nuclear radius (R) is given by the equation:

Where R₀ is the radius of the nucleon (1.2 fm) and A is the number of nucleons or atomic mass number of the nucleus.

• The nuclear force holding the protons and neutrons exist for a short diameter range only. Thus, to maintain stability, the particles are arranged in a manner to keep the dimensions as small as possible. Hence the shape of a nucleus is spherical. 

EXPLANATION:

The nuclear radius is related to the atomic mass number of the nucleus by the equation: ​​

       ----(1)

Since a nucleus is spherical in shape, the volume (V) of the nucleus = 

Where R is the radius of the nucleus.​​

      ----(2)

Using (1) and (2) we get,

Therefore V is directly proportional to A.