The approximate radius of a H-atom is 0.05 nm, and that of proton is 1.5 ×10-15m. Assuming both the hydrogen atom and the proton to be spherical, calculate fraction of the space in an atom of hydrogen that is occupied by the nucleus.

Question

The approximate radius of a H-atom is 0.05 nm, and that of proton is 1.5 ×10-15m. Assuming both the hydrogen atom and the proton to be spherical, calculate fraction of the space in an atom of hydrogen that is occupied by the nucleus. (A) 2.7 × 10-14 (B) 2.7 × 10-10 (C) 5 × 10-14 (D) 2 × 10-16

Tardigrade Admin · Accepted Answer

(Vnucleus/Vatom)=((4/3) π r31/(4)3π r23)=((1.5×10-15/0.5×10-10))3=2.7×10-14

Q. The approximate radius of a $H$ -atom is $0.05 nm$ , and that of proton is $1.5 \times 1 0^{- 15}$ m. Assuming both the hydrogen atom and the proton to be spherical, calculate fraction of the space in an atom of hydrogen that is occupied by the nucleus.

$2.7 \times 1 0^{- 14}$

$2.7 \times 1 0^{- 10}$

$5 \times 1 0^{- 14}$

$2 \times 1 0^{- 16}$

$\frac{V _{n u c l e u s}}{V _{a t o m}} = \frac{\frac{4}{3} π r _{1}^{3}}{\frac{4}{3} π r _{2}^{3}} = (\frac{1.5 \times 1 0 ^{- 15}}{0.5 \times 1 0 ^{- 10}})^{3} = 2.7 \times 1 0^{- 14}$

Q. The approximate radius of a H-atom is 0.05nm, and that of proton is 1.5×10−15m. Assuming both the hydrogen atom and the proton to be spherical, calculate fraction of the space in an atom of hydrogen that is occupied by the nucleus.

2.7×10−14

2.7×10−10

5×10−14

2×10−16