I need help with question below

Question

An atom has a diameter of 3.50 Å3.50 Å and the nucleus of that atom has a diameter of 3.50×10−5 Å3.50×10−5 Å. Determine the fraction of the volume of the atom that is taken up by the nucleus. Assume the atom and the nucleus are a sphere.

Calculate the density of a proton, given that the mass of a proton is 1.0073 amu1.0073 amu and the diameter of a proton is 1.71×10−15 m1.71×10−15 m.

Answer 1

To calculate the volume of a sphere, we use V = 4/3 π r³

V_a = volume of atom = ?

r_a = radius of atom = 1/2 x 3.50 A^o = 1.75 A^o

V_a = 4/3(3.14)(1.75 A^o)³ = 22.4 cubic A^o

V_n = volume of nucleus = ?

r_n = radius of nucleus = 1/2 x 3.5x10^-5 A^o = 1.75x10^-5 A^o

V_n = 4/3(3.14)(1.75x10^-5 A^o)³ = 2.24x10^-14 cubic A^o

Fraction of the atom taken up by the nucleus = 2.24x10^-14 cubic A^o / 22.4 cubic A^o = 1x10^-15

Density of proton = mass of proton / volume of proton

mass = 1.0073

volume = 4/3 π r³ = 4/3(3.14)(8.55x10^-16 A^o)³ = 2.6x10^-45 cubic Aº

Density of the proton = 1.00 amu / 2.6x10^-45 cubic Aº = 3.85x10⁴⁴ amu / cubic Aº