Question

The single proton that forms the nucleus of the hydrogen atom has a radius of approximately . The hydrogen atom itself has a radius of approximately 52.9 .What fraction of the space within the atom is occupied by the nucleus?

Answer 1

To work out the fraction you need to work out the volume of the proton and the volume of the atom. Because the electron around the proton is orbiting it forms a spherical electron density (A sphere) although at any set time its just a particle around the proton.

volume = (4/3) x PI x (r (to the power of 3))

Volume of atom = 4/3 x pi x 52.9pm x 52.9pm x 52.9pm=620091.2818

Volume of proton = 4/3 x pi x 1.0 X 10^-13cm x 1.0 X 10^-13cm x 1.0 X 10^-13cm= 4.19X10^-39

Vol fraction = (volume of proton / Volume of atom) x 100%
=6.76X10^-43

Answer 2

The single proton that forms the nucleus of the hydrogen atom has a radius of approximately . The hydrogen atom itself has a radius of approximately 52.9 .

What fraction of the space within the atom is occupied by the nucleus?

Radius of hydrogen atom = 52.9 x 10^-10 m
Radius of proton is about 1×10^-15 m

Since volume is proportional to radius cubed:

Fraction of space = [(1x10^-15)/(52.9 x 10^-10)]^3 = 6.755 x 10 ^-21