Question

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.

• A. A : B
• B. √A : √B
• C. A² : B²
• D. 1 : 1

Answer 1

The Correct Option is D

To determine the density ratio of two nuclei with mass numbers \(A\) and \(B\), we need to use the principle that nuclear density is a property that does not significantly change from one nucleus to another. The nuclear density is primarily dependent on the nuclear forces and is consistent across different nuclei. The density (\(\rho\)) of a nucleus can be expressed as:

\[\rho = \frac{\text{Mass of the nucleus}}{\text{Volume of the nucleus}}\]

Given that the volume of a nucleus is proportional to its mass number (\(A\)) raised to the power of \(1/3\) (because volume scales with the cube of the radius, and the radius \(r\) is proportional to \(A^{1/3}\)), both the volume and mass for any nucleus scale in the same way. The nuclear density is thus:

\[\rho \propto \frac{A}{A^{1/3}} = A^{0} = \text{constant}\]

As this shows that the density is constant for nuclei with different mass numbers, the density ratio for any two nuclei, regardless of their mass numbers \(A\) and \(B\), remains 1:1.

Therefore, the answer is: 1 : 1