If the radius of a nucleus with mass number $125$ is $1.5 F e r m i$ , then radius of a nucleus with mass number $64$ is

0.48 F e r m i

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0.96 F e r m i

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1.92 F e r m i

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1.2 F e r m i

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Solution

The correct option is D $1.2 F e r m i$
Given : $R_{1} = 1.5 F e r m i$ $A_{1} = 125$ $A_{2} = 64$
Radius of nucleus, $R \propto A^{1 / 3}$
$⟹$ $\frac{R_{2}}{R_{1}} = \frac{A_{2}^{1 / 3}}{A_{1}^{1 / 3}}$

$⟹$ $\frac{R_{2}}{1.5} = \frac{64^{1 / 3}}{125^{1 / 3}}$

$⟹$ $\frac{R_{2}}{1.5} = \frac{4}{5}$

$⟹ R_{2} = 1.2 F e r m i$

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If the radius of a nucleus with mass number 125 is 1.5 Fermi, then radius of a nucleus with mass number 64 is

The correct option is D 1.2 FermiGiven : R1=1.5 Fermi A1=125 A2=64Radius of nucleus, R∝A1/3⟹ R2R1=A1/32A1/31⟹ R21.5=641/31251/3⟹ R21.5=45 ⟹R2=1.2 Fermi

If the radius of a nucleus with mass number $125$ is $1.5 F e r m i$ , then radius of a nucleus with mass number $64$ is