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.

$Density = \frac{Mass}{Volume}$        (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 = $1.66\times 10^{-24} g$

Mass of carbon = $12.00 \times 1.66\times 10^{-24}$

= $19.92\times 10^{-24} g$

=  $1.992\times 10^{-23} g$

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

Density of carbon nucleus =  $\frac{1.992\times 10^{-23} g}{9.9 \times 10^{-39} mL}$  

= $0.201 \times 10^{16} g/mL$

= $2.01 \times 10^{15} g/mL$

Hence, density of carbon nucleus = $2.01 \times 10^{15} g/mL$