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 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 is
`6.23*10^(-31)\ m^3`

(b). The volume of the nucleus is
`4.18*10^(-45)\ m^3`

(c). The percentage of the volume of the atom that is occupied by the nucleus is
`6.70*10^(-13)`

Step-by-step explanation:

Given that,

Radius of nucleus
`r_(n)=1*10^(-15)\ m`

Radius of atom
`r=5.3*10^(-11)\ m`

(a). We need to calculate the volume of the atom

Using formula of volume of the atom

`V=(4\pi* r^3)/(3)`

Where, r = radius of atom

Put the value into the formula

`V=(4\pi*(5.3*10^(-11))^3)/(3)`

`V=6.23*10^(-31)\ m^3`

(b). We need to calculate the volume of the nucleus

Using formula of volume of the nucleus

`V'=(4\pi* r^3)/(3)`

Where, r = radius of atom

Put the value into the formula

`V'=(4\pi*(1*10^(-15))^3)/(3)`

`V'=4.18*10^(-45)\ m^3`

(c). We need to calculate the percentage of the volume of the atom that is occupied by the nucleus

`percentage=(V')/(V)*100`

Put the value into the formula

`percentage=(4.18*10^(-45))/(6.23*10^(-31))*100`

`percentage=6.70*10^(-13)`

Hence, (a). The volume of the atom is
`6.23*10^(-31)\ m^3`

(b). The volume of the nucleus is
`4.18*10^(-45)\ m^3`

(c). The percentage of the volume of the atom that is occupied by the nucleus is
`6.70*10^(-13)`