Question

The single proton that forms the nucleus of the H atom has a radius of approximately 1.0 x 10^-13 cm. The H atom itself has a radius of approximately 52.0 pm. What fraction of the space within the atom is occupied by the nucleu?
first convert 52.9 pm to cm
52.9 pm (1cm/1x10611pm) = 5.29 x 10^-10 cm
Then find the volumes
v proton = 4.19 x 10^-39 cm^3
v of atom 4.65 x 10 ^-28 cm^3

Dividing them gave me 9.008 x 10^-12 but 6.8 x 10^15 is the correct answer. Not sure what I did wrong, or if I'm completely off base. Thanks!

Answer 1

It's the unit conversion on the radius of the H atom.

529pm= 52.9 × 10-12m

Multiply by 100 to get cm: (this makes sense, the diameter is about 10^-10 cm)

5.29 × 10-9cm

Then for the volumes, the factors cancel, so we can just do

4π/3

10× 10-13 ) 3 5.29 × io,) x 109 6.SX 10-15