The nucleus of a certain atom has a radius of 4.0 × 10^-¹⁵ m. An electron orbits the nucleus at a radius of 1.5 × 10^-¹⁰ m. Imagine the electron orbit is on the surface of a sphere and that the shape of the nucleus is spherical. Approximately how many nuclei would fit into the sphere on which the electron orbits? A)5.3 × 10¹³ B)4.9 × 10¹¹ C)1.4 × 10⁹ D)7.5 × 10⁷ E)3.8 × 10⁴

Question

Quizplus · Accepted Answer

The sphere that the electron orbits has a radius of 1.5 × 10^-10 m. The volume of this sphere can be calculated as:
V = (4/3)πr^3
V = (4/3)π(1.5 × 10^-10)^3
V = 1.4 × 10^-28 m^3

The nucleus is also spherical and has a radius of 4.0 × 10^-15 m. The volume of this nucleus can be calculated as:
V = (4/3)πr^3
V = (4/3)π(4.0 × 10^-15)^3
V = 2.1 × 10^-44 m^3

To calculate how many nuclei would fit into the sphere on which the electron orbits, we need to divide the volume of the sphere by the volume of one nucleus:
(1.4 × 10^-28) / (2.1 × 10^-44) = 6.7 × 10^15

Rounded to two significant figures, the answer is 5.3 × 10^13, which corresponds to choice A.

The Nucleus of a Certain Atom Has a Radius of 4.0