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The nucleus of an atom is spherical. T...

The nucleus of an atom is spherical. The relation between radius of the nucleus and mass number A is given by `1.25xx10^(-13)xxA^((1)/(3))cm`. If radius of atom is one`Å` and the mass number is 64, then the fraction of the atomic volume that is occupied by the nucleus is `(x)xx10^(-13)`. Calculate x

A

`1.0xx10^(-3)`

B

`5.0xx10^(-5)`

C

`2.5xx10^(-2)`

D

`1.25xx10^(-13)`

Text Solution

Verified by Experts

The correct Answer is:
D
Radius of nucleus = `1.25xx10^(-13)xxA^(1//3)cm`
= `1.25xx10^(-13)xx64^(1//3)=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))`
= `1.25xx10^(-13)`
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