Question

Two nuclei have mass numbers in the ratio 1:8. what is the ratio of their nuclear radii?

Answer 1

Given,

A1/A2 = 1/8

so, ratio of nuclear radii is -

R1/R2 = A1/A2^1/3

         = (1/2^3)^1/3

         = 1/2

now, ratio of densities is -

d1/d2 = 1/1

Answer 2

Answer:

The nuclear radii have a 1:2 ratio.

Explanation:

The relationship between nuclear radius and mass number is given as,

$\frac{R_1}{R_2}=\sqrt[3]{\frac{A_1}{A_2} }$     (1)

Where,

R₁, R₂=respective nuclear radii

A₁, A₂=respective mass number of the nuclei

From the question we have,

$\frac{A_1}{A_2}=\frac{1}{8}$     (2)

When we plug in equation (2) into equation (1), we get:

$\frac{R_1}{R_2}=\sqrt[3]{\frac{1}{8} }$

$\frac{R_1}{R_2}=\frac{1}{2}$

Hence, the ratio of the nuclear radii is 1:2.

#SPJ2