Question

The volume of the nucleus of a carbon atom is about 9.9 10⁻³⁹. the molar mass of carbon is 12.00 g mol⁻¹. what is the density of the carbon nucleus?

Answer 1

Density is defined as the ratio of mass to the volume.

`Density = (Mass)/(Volume)` (1)

Since, molar mass of carbon is given i.e.
`12.00 g mol^(-1)`, determine the mass of carbon, we get

1 amu = 1 g/mol

1 amu =
`1.66* 10^(-24) g`

Mass of carbon =
`12.00 * 1.66* 10^(-24)`

=
`19.92* 10^(-24) g`

=
`1.992* 10^(-23) g`

Now, put the value of mass and volume in formula (1)

Density of carbon nucleus =
`(1.992* 10^(-23) g)/(9.9 * 10^(-39) mL)`

=
`0.201 * 10^(16) g/mL`

=
`2.01 * 10^(15) g/mL`

Hence, density of carbon nucleus =
`2.01 * 10^(15) g/mL`