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

This question was previously asked in
CUET Physics 18th Aug 2022 Official Paper
View all CUET Papers >
  1. \(\frac{R_1}{R_2}=\frac{3}{2}\)
  2. \(\frac{R_1}{R_2}=\frac{4}{2}\)
  3. \(\frac{R_1}{R_2}=\frac{6}{4}\)
  4. \(\frac{R_1}{R_2}=\frac{\sqrt3}{2}\)

Answer (Detailed Solution Below)

Option 1 : \(\frac{R_1}{R_2}=\frac{3}{2}\)
Free
CUET General Awareness (Ancient Indian History - I)
11.2 K Users
10 Questions 50 Marks 12 Mins

Detailed Solution

Download Solution PDF

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.

 

Latest CUET Updates

Last updated on Jun 13, 2025

-> Check out the CUET UG Answer Key 2025.

-> The CUET 2025 Postponed for 15 Exam Cities Centres.

-> The CUET 2025 Exam Date was between May 13 to June 3, 2025. 

-> 12th passed students can appear for the CUET UG exam to get admission to UG courses at various colleges and universities.

-> Prepare Using the Latest CUET UG Mock Test Series.

-> Candidates can check the CUET Previous Year Papers, which helps to understand the difficulty level of the exam and experience the same.

Get Free Access Now
Hot Links: teen patti comfun card online all teen patti game mpl teen patti teen patti star