Two nuclei have mass numbers A and B respectively. The density ratio of the nuclei is ______________.
Fill in the blank with the correct answer from the options given below.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 1 : 1 \)
The nuclear radius grows as the cube root of the mass number, \( R = R_0 A^{1/3} \), so the nuclear volume is proportional to \( A \). The mass of a nucleus is also proportional to \( A \) (about \( A\,m \), with \( m \) the mass of a nucleon).
\( \displaystyle \rho = \frac{A\,m}{\frac{4}{3}\pi R_0^{3} A} = \frac{3m}{4\pi R_0^{3}} \)
The mass number cancels, so the nuclear density is the same for all nuclei, and the ratio is \( 1 : 1 \).
NCERT (2026-27):
Size of the Nucleus – “… 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.”