Question

Carbon-12 contains 6 protons and 6 neutrons. The radius of the nucleus is approximately 2.7 fm (femtometers) and the radius of the atom is approximately 70 pm (picometers). Calculate the volume of the nucleus and the volume of the atom.

Answer 1

Explanation:

Let us assume that volumes is equal to spheres  volume of nucleus.

fm = femto meter = $10^{-15}$

pm = pico meter = $10^{-12}$

Hence, calculate the volume as follows.

          V = $\frac{4}{3} \times \pi \times r^{3}$

              = $\frac{4}{3} \times 3.14 \times (2.7)^{3}$

              = 82.4481 $fm^{3}$ (cubic femtometers)

or,          = 82 $fm^{3}$

Now, we will calculate the volume of the atom as follows.

          V = $\frac{4}{3} \times \pi \times r^{3}$

             = $\frac{4}{3} \times 3.14 \times (70)^{3}$

             = 1436758.4 $pm^{3}$ (cubic picometers)

thus, we can conclude that volume of the nucleus is 82 $fm^{3}$  and volume of the atom is 1436758.4 $pm^{3}$.