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 × 10-13 × A1 / 3 cm . Radius of atom is 1 mathring A. If the mass number is 64, then the fraction of the atomic volume that is occupied by the nucleus is

Question

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 × 10-13 × A1 / 3 cm . Radius of atom is 1 mathring A. If the mass number is 64, then the fraction of the atomic volume that is occupied by the nucleus is (A) 1.0 × 10-3 (B) 5.0 × 10-5 (C) 2.5 × 10-2 (D) 1.25 × 10-13

Tardigrade Admin · Accepted Answer

Radius of nucleus =1.25 × 10-13 ×(64)1 / 3 Radius of atom =1 mathringA=1 × 10-8 × 10-13 cm Fraction of volume =( text Volume of nucleus / text Volume of atom ) =((4/3) π(5 × 10-13)3/(4)3 π(1 × 10-8)3) =(125 × 10-39/10-24)=1.25 × 10-13

$1.0 \times 1 0^{- 3}$

$5.0 \times 1 0^{- 5}$

$2.5 \times 1 0^{- 2}$

$1.25 \times 1 0^{- 13}$

Q. The nucleus of an atom can be assumed to be spherical. The radius of the nucleus of mass number A is given by 1.25×10−13×A1/3cm. Radius of atom is 1A˚. If the mass number is 64, then the fraction of the atomic volume that is occupied by the nucleus is

1.0×10−3

5.0×10−5

2.5×10−2

1.25×10−13

Radius of nucleus =1.25×10−13×(64)1/3 Radius of atom =1A˚=1×10−8×10−13cm Fraction of volume = Volume of atom Volume of nucleus ​ =34​π(1×10−8)334​π(5×10−13)3​ =10−24125×10−39​=1.25×10−13

$1.0 \times 1 0^{- 3}$

$5.0 \times 1 0^{- 5}$

$2.5 \times 1 0^{- 2}$

$1.25 \times 1 0^{- 13}$