Question

An atom has a diameter of 1.00 Å and the nucleus of that atom has a diameter of 8.00×10^−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

Answer 1

Answer:

5.122 × 10⁻¹³

Explanation:

Sphere volume is calculated with the formula:

$V = \frac{4}{3}$ π $r^{3}$

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