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Atomic Number and Mass Number

What will be ...

Question

What will be the ratio of the radii of two nuclei of mass numbers $A_{1}$ and $A_{2}$ ?

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Solution

The radius of nucleus of an atom of mass number $A$ is given by $R = R_{o} (A)^{1 / 3}$ where $R_{o}$ is a unique constant $= 1.2 \times 10^{- 15} m$ . Hence $R α (A)^{1 / 3}$
So, ratio of radii of two nuclei with mass number $A_{1}$ and $A_{2}$ is
$R_{1} / R_{2} = (A_{1} / A_{2})^{1 / 3}$

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