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).

Part A Calculate the volume of the nucleus and the volume of the atom. (Assume two significant figures.) Express your answers using two significant figures separated by a comma.

Part B What percentage of the carbon atom's volume is occupied by the nucleus? (Assume two significant figures.) Express your answer using two significant figures.

Answer 1

A)

Assume volumes = spheres

volume of nucleus

fm = femto meter = 10^-15;

pm = pico meter = 10^-12

Calculate volume to

V = 4/3*PI*(R^3)

V = (4/3*3.1416)(2.7^3)

V = 82.4481 fm^3 (cubic femtometers)

2 sig fig --> 82 fm3

volume of the atom:

V = 4/3*PI*(R^3)

V = (4/3*3.1416)(70^3)

V = 1436758.4 pm^3 (cubic picometers)

B)

% of nucleus in atom = volume of nuecleu / volume of atom

volume of atom --> 1436758.4

volume of nucleus = 82.4481 fm3

1 fm3 = 10^-9 pm3

82.4481 fm3 * (10^-9 pm3 / fm3 ) = 82.4481 *10^-9 pm3

Now,

% = ( 82.4481 *10^-9 ) / 82.4481 * 100 = 10^-7 %