Question

An alpha particle is the same as a helium-4 nucleus: it contains two protons and two neutrons in the nucleus. Given that the radius of an alpha particle is approximately 2.6 fm, calculate the density of an alpha particle in units of grams per cubic centimeter.

Answer 1

1.31x10¹¹ g/cm³

Step-by-step explanation:

The mass of the proton is equal to the mass of the neutron, which is 1.67x10⁻²⁴ g, so the mass of the alpha particle is 4*1.67x10⁻²⁴ = 6.68x10⁻²⁴ g.

1 fm = 1.0x10⁻²³ cm, thus the radius of the alpha particle is 2.3x10⁻¹² cm. If the particle is a sphere, the volume of it is:

V = (4/3)*π*r³, where r is the radius, so:

V = (4/3)*π*(2.3x10⁻¹²)³

V = 5.1x10⁻³⁵ cm³

The density of the particle is the how mass exists per unit of volume, so, it's the mass divided by the volume:

d = 6.68x10⁻²⁴/5.1x10⁻³⁵

d = 1.31x10¹¹ g/cm³