A nucleus of mass number 27 has a radius R . If another nucleus has...

The radius of a nucleus $R$ is related to its mass number $A$ by the relation:
$R = R_{0}A^{\dfrac{1}{3}}$

For the first nucleus:
$R_{1} = R = R_{0}(27)^{\dfrac{1}{3}}$

For the second nucleus:
$R_{2} = 2R = R_{0}(A_{2})^{\dfrac{1}{3}}$

Taking the ratio of the two radii:
$\dfrac{R_{2}}{R_{1}} = \left(\dfrac{A_{2}}{27}\right)^{\dfrac{1}{3}}$

$2 = \left(\dfrac{A_{2}}{27}\right)^{\dfrac{1}{3}}$

Cubing both sides, we get:
$8 = \dfrac{A_{2}}{27}$

$A_{2} = 27 \times 8 = 216$

Answer: $216$