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

Options

A. `2.7 xx 10^-14`
B. `2.7 xx 10^-10`
C. `5 xx 10^-14`
D. `2 xx 10^-16`

Answer

A

Explanation

(a) `(V_("nucleus"))/(V_("atom")) = ((4)/(3) pi r_1^3)/((4)/(3) pi r_2^3) = ((1.5 xx 10^-15)/(0.5 xx 10^-10))^3 = 2.7 xx 10^-14`.