The ratio of radii of two nuclei having atomic mass numbers 27 and 8 respectively, will be:

Concept:

The ratio of radii of two nuclei can be approximated by the following formula:

\(\frac{r_1}{r_2}~=~(\frac{A_1}{A_2})^{(\frac{1}{3})}\) 

Where r1 and r2 are the radii of the two nuclei, and A1 and A2 are their atomic mass numbers.

Using this formula, we can calculate the ratio of radii of the two nuclei with atomic mass numbers 27 and 8 respectively as follows:

\(\frac{r_1}{r_2}~=~(\frac{A_1}{A_2})^{(\frac{1}{3})}\)

\(\frac{r_1}{r_2}~=~(\frac{27}{8})^{(\frac{1}{3})}\)

\(\frac{r_1}{r_2}~=~\frac{3}{2} \)

Therefore, the ratio of radii of the two nuclei is 1.5 i.e. 3/2.

The correct answer is option (1)

Important Points

• This formula is based on the assumption that the nuclear density is constant for both nuclei.
• It is derived from the fact that the volume of a nucleus is proportional to its mass number, and the radius of a nucleus is proportional to the cube root of its volume.
• However, it should be noted that this formula is only an approximation and may not hold true for all nuclei.