Question Details

Four statements are given (A is mass number):

A. The volume of a nucleus is proportional to A.
B. The volume of a nucleus is proportional to A^1/3.
C. The difference in mass of an atom and its nucleus is called the mass defect.
D. The difference in mass of a nucleus and its constituents is called the mass defect.

Choose the correct answer from the options given below:

Options

A and D are true, but B and C are false

B and D are true, but A and C are false

B and C are true, but A and D are false

A and C are true, but B and D are false

Show Answer

Correct Answer :

Option A

A and D are true, but B and C are false

Solution :

**Statement A – “The volume of a nucleus is proportional to A.”**

Empirically the radius R of a nucleus follows the relation

R = r_0\,A^{\frac{1}{3}}

where r₀ ≈ 1.2 fm is a constant. The volume V of a sphere is

V = \frac{4}{3}\pi R^{3}

Substituting the expression for R,

V = \frac{4}{3}\pi \bigl(r_0\,A^{\frac{1}{3}}\bigr)^{3}
      = \frac{4}{3}\pi r_0^{3}\,A

All the constants combine into a single factor, leaving

V \propto A

Thus the volume is directly proportional to the mass number A, so **Statement A is true**.

**Statement B – “The volume of a nucleus is proportional to A^1/3.”**

From the derivation above, the volume depends on A, not on A^1/3. The proportionality V ∝ A^1/3 would follow only for the radius, not the volume. Therefore **Statement B is false**.

**Statement C – “The difference in mass of an atom and its nucleus is called the mass defect.”**

The term *mass defect* refers to the loss of mass when separate nucleons (protons and neutrons) bind together to form a nucleus. It is the difference between the summed masses of the free nucleons and the actual mass of the **nucleus**. The atom also includes the electron cloud, whose mass is negligible compared with nuclear mass, but the definition does not involve the atom–nucleus mass difference. Hence **Statement C is false**.

**Statement D – “The difference in mass of a nucleus and its constituents is called the mass defect.”**

This matches the standard definition: the mass defect equals the sum of the masses of the separate protons and neutrons minus the measured mass of the bound nucleus. Therefore **Statement D is true**.

Combining the results, the only correct combination is that **A and D are true, while B and C are false**.