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The nucleus of an atom is spherical. The relation between radius of the nucleus and mass number A is given by 1.25 × 1 0 - 13 × A 1 3 c m . 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 × 1 0 - 13 . Calculate x

Correct answer

1.25

Step-by-step solution

Radius of nucleus = 1.25 × 1 0 - 13 × A 1 3 c m = 1.25 × 1 0 - 13 × 6 4 1 3 = 5 × 1 0 - 13 c m Radius of atom = 1 Å = 1 0 - 8 c m . Volume of nucleus Volume of atom = 4 3 π ( 5 × 1 0 - 13 ) 3 4 3 π ( 1 0 - 8 ) 3 = 1.25 × 1 0 - 13 .

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