Two nuclei have mass numbers in the ratio 27:125 . The ratio of their nuclear radii would be:

Question

Two nuclei have mass numbers in the ratio 27:125 . The ratio of their nuclear radii would be: (A) 5:9 (B) 9:5 (C) 5:3 (D) 3:5

Tardigrade Admin · Accepted Answer

Here , A1:A2=27:125 ⇒ (A1/A2)=(27/125) Since, R = R0 A1 / 3 ∴ (R1/R2)=(A11/3/A21/3)=(. (A1/A2) .)1/3 =(. (27/125) .)1/3 =(3/5) ∴ The ratio of their radii = 3: 5

Q. Two nuclei have mass numbers in the ratio $27 : 125$ . The ratio of their nuclear radii would be:

$5 : 9$

$9 : 5$

$5 : 3$

$3 : 5$

Here ,
$A_{1} : A_{2} = 27 : 125 \Rightarrow \frac{A _{1}}{A _{2}} = \frac{27}{125}$
Since, $R = R_{0} A^{1/3}$
$∴ \frac{R _{1}}{R _{2}} = \frac{A _{1}^{1/3}}{A _{2}^{1/3}} = (\frac{A _{1}}{A _{2}})^{1/3} = (\frac{27}{125})^{1/3} = \frac{3}{5}$
$∴$ The ratio of their radii = 3 : 5

Q. Two nuclei have mass numbers in the ratio 27:125 . The ratio of their nuclear radii would be:

5:9

9:5

5:3

3:5