Question

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 spheres.

Given that the fraction of atomic volume is 2.54×10 ¹³, which of the following statements is correct

a) The nucleus occupies the entire volume of the atom.

b) The nucleus occupies a negligible fraction of the atom's volume.

c) The nucleus occupies approximately 2.54×10 ¹³ times the volume of the atom.
d) The nucleus occupies approximately 7.50×10 −⁵ times the volume of the atom.

Answer 1

The nucleus occupies a negligible fraction of the atom's volume because its radius is about 10^-5 times that of the atom, resulting in a volume that is 10^-15 times smaller than the atom's volume.

Step-by-step explanation:

To determine the fraction of the volume of an atom that is taken up by the nucleus, we must consider the sizes of the atom and the nucleus. The diameter of an atom is approximately 10-10 meters, while the diameter of a nucleus is about 10-15 meters. Given that both the atom and the nucleus can be approximated as spheres, the volume of a sphere is calculated using the formula V = (4/3)πr3, where r is the radius of the sphere.

Based on the information given, the fraction of the atomic volume taken up by the nucleus is 2.54×1013. However, since the radius of the nucleus is about 10-5 times that of the atom, the volume of the nucleus would be (10-5)3 = 10-15 times the volume of the atom. This demonstrates that the nucleus occupies a negligible fraction of the atom's volume.