If r₁ and r₂ are the radii of the atomic nuclei of mass numbers 64 and 125 respectively, then the ratio ( r₁/ r₂ ) is

$\frac{64}{125}$

$\sqrt{\frac{64}{125}}$

$\frac{5}{4}$

$\frac{4}{5}$

Solution

$\frac{4}{5}$

Nucleus of mass number A has a radius

$R = R_{o} {(A)}^{\frac{1}{3}}$

Atomic mass number A₁ =64

${(64)}^{\frac{1}{3}}$ = 4

Atomic mass number A₂ = 125

${(125)}^{\frac{1}{3}} = 5$

∴ $\frac{r_{1}}{r_{2}} = {(\frac{A_{1}}{A_{2}})}^{\frac{1}{3}}$

= ${[{(\frac{4}{5})}^{3}]}^{\frac{1}{3}}$

$\frac{r_{1}}{r_{2}} = \frac{4}{5}$

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