Question

The single proton that forms the nucleus of the hydrogen atom has a radius of approximately 1.0 X 10- 13 em. The hydrogen atom itself has a radius of approximately 52.9 pm. What fraction of the space within the atom is occupied by the nucleus?

Answer 1

Answer:
`0.51*10^(-15)`

Explanation:

We consider the shape of nucleus and the atom to be sphere.

Also , we know that the Volume of sphere =
`V=(4\pi)/(3)r^3`

Given : Radius of proton :
`r=1.0*10^(-3)\text{ em}`

Since 1 em = 0.0042175176 metres

∴
`r=1*10^(-13)* 0.0042175176\approx4.22*10^(-16) \text{ m}`

Radius of atom :
`R=52.9 \text{ pm}`

Since,
`1\ \text{pm}=1*10^(-12)`

∴Radius of atom :
`R=52.9*10^(-12) =5.29*10^(-11)\text{ m}`

Now, the fraction of the space within the atom is occupied by the nucleus :_

`(V(r))/(V(R))=((4\pi)/(3)(4.22*10^(-16) )^3)/((4\pi)/(3)(5.29*10^(-11))^3)\\\\=((4.22)/(5.29))^3*(10^(-48))/(10^(-33))\\\\\approx0.51*10^(-48+33)=0.51*10^(-15)`