Question

The radius of a carbon nucleus is about (3 × 10⁻¹⁵) m, and its mass is (12 ,amu). Determine the average density of the nuclear material.

A) (4 × 10¹⁷ ,kg/m³)
B) (6 × 10¹⁶ ,kg/m³)
C) (2 × 10¹⁸ ,kg/m³)
D) (8 × 10¹⁵ ,kg/m³)

Answer 1

The average density of the carbon nucleus is approximately 4 × 10^17 kg/m³. The correct option is A).

Step-by-step explanation:

Protons and neutrons, collectively called nucleons, are packed together tightly in a nucleus. With a radius of about 10-15 meters, a nucleus is quite small compared to the radius of the entire atom, which is about 10-10 meters. Nuclei are extremely dense compared to bulk matter, averaging 1.8 × 1014 grams per cubic centimeter. To calculate the average density of the nuclear material, we can use the formula:

Density = mass/volume

The mass of the carbon nucleus is 12 atomic mass units (amu). The volume can be calculated using the formula for the volume of a sphere:

Volume = (4/3)πr3

Substituting the values into the formulas, we get:

Density = 12 amu / ((4/3)π(3x10-15)3)

Calculating the expression gives us a density of approximately 4 × 1017 kg/m³.