Question

carbon -12 contains 6 protons and 6 nuetrons. 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. What percentage of the carbon atom's volume is occupied by the nucleus?

Answer 1

Using formula for volume,

Volume = (4/3).pi.r^3

For nucleus, r = 2.7 fm = 0.0027 pm

Volume of nucleus = (4/3) x 3.24 x (0.0027)^3 = 8.24 x 10^-8 pm^3

For atom, r = 70 pm

Volume of arom = (4/3) x 3.14 x (70)^3 = 1.44 x 10^6 pm^3

Percentage of carbon atom's volume occupied by nucleus = (volume of nucleus/volume of atom) x 100

= (8.24 x 10^-8/1.44 x 10^6) x 100 = 5.72 x 10^-12

Other way,

If we convert 70 pm = 70,000 fm

we get,

percent (volume nucleus/volume atom) x 100 = (82.41/1.44 x 10^15) x 100 = 5.74 x 10^-14