The hydrogen atom contains 1 proton and 1 electron. The radius of the proton is approximately 1.0 fm (femtometers), and the radius of the hydrogen atom is approximately 53 pm (picometers).

Calculate the volume of the nucleus and the volume of the atom for hydrogen.

What percentage of the hydrogen atom's volume is occupied by the nucleus?

 

Answer:

1.

volume of sphere= 4/3 * pi * r^3

V = (4π/3)(5.3x10^-9 cm)^3 = 6.24x10^-25 cm^3

and

Percentage of hydrogen atoms volume = [(1.41x10^-38 cm^3) / (6.24x10^-25 cm^3)] x 100% = 2.26x10^-8 %

2.

You know volume of a sphere V = 4/3 π r³

For the nucleus V = 4.189 * (1.0)³ = 4.189 fm³

For the atom V = 4.189 * (53)³ = 6.236 * 10^5 fm³

Proton volume = 4/3 π (1e-15)^3 = 4.188e-45 m^3 

Atomic volume = 4/3 π (5.3e-11)^3 = 6.2e-31 m^3 

100% * 4.188e-45 / 6.2e-31 = 6.7e-13 %

6.7e-13 % of the hydrogen atom's volume is occupied by the nucleus