Question

Calculate the ratio of radii of two nuclei with mass number in the ratio 8:27

Answer 1

Answer:

Radius of nucleus is proportional to cube root of mass number (R∝A1/3)(R∝A1/3) . Hence ratio of radii becomes 2 :3

Explanation:

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Answer 2

Solution :-

We know :-

$\bf \star \: R = R_0 {A}^{ \sf\frac{1}{3} }$

$\sf R_1 = R_0 {8}^{ \sf\frac{1}{3} } \: \: \: \: \: \: \: \: ....(1)$

$\sf R_2 = R_0 {27}^{ \sf\frac{1}{3} } \: \: \: \: \: \: \: \: ....(2)$

Divide eq(1) by eq(2),

$: \sf \implies \dfrac{R_1}{R_2} = \left( \dfrac{8} {27}\right) ^{ \sf \frac{1}{3} }$

$: \sf \implies \dfrac{R_1}{R_2} = \dfrac{2}{3}$

$\bf R_1 : R_2= 2 : 3$