Question

The nucleus of the hydrogen atom has a radius of about
1 x 10^-15 m. The electron is normally at a distance of about 5.3 x 10^-11 m
from the nucleus. Assuming that the hydrogen atom is a sphere with a
radius of 5.3 x 10^-11 m, find (a) the volume of the atom, (b) the
volume of the nucleus, and (c) the percentage of the volume of the
atom that is occupied by the nucleus.The nucleus of the hydrogen atom has a radius of about
1 x 10^-15 m. The electron is normally at a distance of about 5.3 x 10^-11 m
from the nucleus. Assuming that the hydrogen atom is a sphere with a
radius of 5.3 x 10^-11 m, find (a) the volume of the atom, (b) the
volume of the nucleus, and (c) the percentage of the volume of the
atom that is occupied by the nucleus.

Answer 1

(a)

the volume of the atom

V = 4/3?r^3

     here r = 5.5*10^-11 m

     = 4/3*3.142*(166.375)*10^-33

     = 697.0*10^-33 m^3

(b)

the volume of the nucleus

V = 4/3?r^3

     here r = 1.1*10^-15 m

     = 4/3*3.142*(1.331)*10^-45

     =  5.576*10^-45 m^3

(c)

the % of the volume occupied by the nucleus
V2/V1 * 100 = 5.576*10^-45 m^3/ 697.0*10^-33 m^3*100

                     = 0.8*10^-12 %

(d)

The distance the proton has to travel to reach the surface of the nucleus is equal to the wavelength ? and its value is ?=(55000 - 1.1) x 10^-15m=54998.9 x10^-15m.

The work done in electron volts is E=hc/?=6.626 x10^-34 x 3 x 10⁸/54998.9 x 10^-15

E=3.614 x 10^-15J