Which of the following are correct?
(A) Nuclear density is not constant for all matter.
(B) Nuclear density is around \( 2.3\times10^{17}\ \mathrm{kg/m^{3}} \).
(C) Nuclear density is very large compared to the density of ordinary matter.
(D) The mass of ordinary matter is mainly due to nucleus.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (B), (C) and (D) only
The radius of a nucleus is \( R = R_{0}A^{1/3} \), so its volume is proportional to the mass number A, and so is its mass. Their ratio, the nuclear density, is therefore the same for all nuclei.
\( \displaystyle \rho = \frac{m\,A}{\frac{4}{3}\pi R_{0}^{3}A} = \frac{m}{\frac{4}{3}\pi R_{0}^{3}} \approx 2.3\times10^{17}\ \mathrm{kg/m^{3}} \)
(A) Nuclear density is not constant for all matter. — Incorrect. A cancels, so the density is the same for all nuclei.
(B) Nuclear density is around \( 2.3\times10^{17}\ \mathrm{kg/m^{3}} \). — Correct. This is the value obtained with \( R_{0} \approx 1.2\ \mathrm{fm} \) and m about 1 u per nucleon.
(C) Nuclear density is very large compared to the density of ordinary matter. — Correct. Ordinary matter is about \( 10^{3}\ \mathrm{kg/m^{3}} \), some \( 10^{14} \) times less dense.
(D) The mass of ordinary matter is mainly due to nucleus. — Correct. Electrons contribute only about 1/1840 of the mass of each nucleon, so almost all of an atom’s mass is in its tiny nucleus.
NCERT (2026-27):
Size of the Nucleus – “… Thus the density of nucleus is a constant, independent of \( A \), for all nuclei. … The density of nuclear matter is approximately \( 2.3\times10^{17}\,\mathrm{kg\,m^{-3}} \). This density is very large compared to ordinary matter, say water, which is \( 10^{3}\,\mathrm{kg\,m^{-3}} \).”
Summary – “… More than 99.9% mass of the atom is concentrated in the nucleus.”