Q138 / 180 · NEET 2026 (Cancelled) · Physics
Four statements are given (A is mass number) :
A. The volume of a nucleus is proportional to $A^{1/3}$.
B. The volume of a nucleus is proportional to $A$.
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 :
A. The volume of a nucleus is proportional to $A^{1/3}$.
B. The volume of a nucleus is proportional to $A$.
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 :
- AA and C are true, but B and D are false
- BB and C are true, but A and D are false
- CA and D are true, but B and C are false
- Correct answerDB and D are true, but A and C are false
Solution
The radius of a nucleus is given by $R = R_0 A^{1/3}$.
The volume of the nucleus is $V = \dfrac{4}{3} \pi R^3 = \dfrac{4}{3} \pi R_0^3 A$.
Thus, the volume of a nucleus is directly proportional to its mass number $A$. Statement A is false and Statement B is true.
The mass defect is defined as the difference between the sum of the masses of the constituent nucleons (protons and neutrons) and the actual mass of the nucleus.
Thus, Statement C is false and Statement D is true.
Therefore, B and D are true, but A and C are false.
Answer: B and D are true, but A and C are false
The volume of the nucleus is $V = \dfrac{4}{3} \pi R^3 = \dfrac{4}{3} \pi R_0^3 A$.
Thus, the volume of a nucleus is directly proportional to its mass number $A$. Statement A is false and Statement B is true.
The mass defect is defined as the difference between the sum of the masses of the constituent nucleons (protons and neutrons) and the actual mass of the nucleus.
Thus, Statement C is false and Statement D is true.
Therefore, B and D are true, but A and C are false.
Answer: B and D are true, but A and C are false
Hence, the correct answer is option: 'D'.