Which of the following statements are correct?
A. Nuclear density is a constant for all matter.
B. Nuclear density is around 2.3×1015 kg/m3.
C. Nuclear density is very large compared to ordinary matter.
D. The radius of the nucleus is proportional to A1/3, where A is the Atomic Mass number.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → A, C and D only
Note: The given answer is as per the official NTA Answer Key. However, none of the given options appears to be correct, because statement (A) is true only for nuclei and not for all matter, as explained below.
The nuclear radius grows as \( R = R_0A^{1/3} \), so the nuclear volume, like the nuclear mass, is proportional to the mass number A. The nuclear density is therefore independent of A, about \( 2.3\times10^{17}\,\mathrm{kg\,m^{-3}} \).
(A) Nuclear density is a constant for all matter. — Correct as per NTA; however, it is not correct as a general statement. The density is the same for all nuclei, but ordinary matter has widely varying densities (water about 1000 kg m−3, iron about 7800 kg m−3).
(B) Nuclear density is around 2.3×1015 kg/m3. — Incorrect. The nuclear density is about \( 2.3\times10^{17}\,\mathrm{kg\,m^{-3}} \), a hundred times the value stated.
(C) Nuclear density is very large compared to ordinary matter. — Correct. It is about \( 10^{14} \) times the density of water.
(D) The radius of the nucleus is proportional to A1/3, where A is the Atomic Mass number. — Correct. This is the relation \( R = R_0A^{1/3} \), with A the mass number.
So strictly only (C) and (D) are correct, which is not an option; NTA’s Option (4) holds only if (A) is read as “nuclear density is the same for all nuclei”.
NCERT (2026-27):
Size of the Nucleus – “… It has been found that a nucleus of mass number A has a radius
\( \displaystyle R = R_0 A^{1/3} \qquad (13.5) \)
where \( R_0 = 1.2 \times 10^{-15}\,\mathrm{m} \) (=1.2 fm; 1 fm = 10–15 m). This means the volume of the nucleus, which is proportional to R3 is proportional to A. Thus the density of nucleus is a constant, independent of A, for all nuclei. Different nuclei are like a drop of liquid of constant density. The density of nuclear matter is approximately 2.3 × 1017 kg m–3. This density is very large compared to ordinary matter, say water, which is 103 kg m–3.”