Two nuclei have mass numbers in the ratio 1:8 . The ratio of their nuclear radii would be:

Question

Two nuclei have mass numbers in the ratio 1:8 . The ratio of their nuclear radii would be: (A) 3:1 (B) 1:3 (C) 1:2 (D) 2:1

Tardigrade Admin · Accepted Answer

A1:A2=1:8 ⇒ (A1/A2)=(1/8) Since , R = R0 A1 / 3 ∴ (R1/R2)=(A11 / 3/A21 / 3) ⇒ (. (A1/A2) .)1 / 3=(. (1/8) .)1 / 3 =(1/2) The ratio of their radii = 1:2 .

Q. Two nuclei have mass numbers in the ratio $1 : 8$ . The ratio of their nuclear radii would be:

$3 : 1$

$1 : 3$

$1 : 2$

$2 : 1$

$A_{1} : A_{2} = 1 : 8 \Rightarrow \frac{A _{1}}{A _{2}} = \frac{1}{8}$
Since ,
$R = R_{0} A^{1/3}$
$∴ \frac{R _{1}}{R _{2}} = \frac{A _{1}^{1/3}}{A _{2}^{1/3}} \Rightarrow (\frac{A _{1}}{A _{2}})^{1/3} = (\frac{1}{8})^{1/3} = \frac{1}{2}$
The ratio of their radii = $1 : 2$ .

Q. Two nuclei have mass numbers in the ratio 1:8 . The ratio of their nuclear radii would be:

3:1

1:3

1:2

2:1