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The nucleus of an atom can be assumed to...

The nucleus of an atom can be assumed to be spherical. The radius of the nucleus of mass number A is given by `1.25 xx 10^(-13) xx A^(1//3)` cm. Radius of atom is one A. If the mass number is 64, then the fraction of the atomic volume that is occupied by the nucleus is

A

`1.0xx10^(-3)`

B

`5.0xx10^(-5)`

C

`2.5xx10^(-2)`

D

`1.25xx10^(-13)`

Text Solution

Verified by Experts

Radius of nucleus = `1.25xx10^(-13)xxA^(1//3)cm`
`=1.25xx10^(-13)xx64^(1//3)` cm
`=1.25xx10^(-13)xx4cm=5xx10^(-13)cm`
Radius of atom = `1Å=10^(-8)cm`
Volume of nucleus/volume of atom
`=((4//3)pi(5xx10^(-13))^(3))/((4//3)pi(10^(-8))^(3))=(125xx10^(-39))/(10^(-24))`
`=125xx10^(-15)=1.25xx10^(-13)`
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