Answer:
5.122 × 10⁻¹³
Explanation:
Sphere volume is calculated with the formula:
[tex]V = \frac{4}{3}[/tex] π [tex]r^{3}[/tex]
V - volume
r - radius
radius = diameter / 2
radius of atom= 1 / 2 = 0.5 Å
radius of nucleus = (8 × 10⁻⁵) / 2 = 4 × 10⁻⁵ Å
now we may calculate the volume for the atom and the nucleus
atom volume = (4/3) × 3.14 × (0.5)³ = 0.523 ų
nucleus volume = (4/3) × 3.14 × (4 × 10⁻⁵)³ = 2.679 × 10⁻¹³ ų
now the fraction of volume of the atom that is taken up by the nucleus:
fraction = nucleus volume / atom volume
fraction = 2.679 × 10⁻¹³ / 0.523 = 5.122 × 10⁻¹³
