Calculate the density of a proton, given that the mass of a proton is 1.0073 amu and the diameter of a proton is 1.73 * 10 ^ - 15 m. The answer should be in g/cm^3

Density = 6.17 * 10^14 g/cm³

Explanation:

Given Parameters

Mass of the proton = 1.0073 amu

Diameter of the proton = 1.75 * 10^-15 m

Required:

Calculate the density of the proton.

Density is calculated using the following formula;

Density = mass / volume

Where mass should be in grams and volume should be in cm ³

Calculating mass of a proton in grams.

Mass = 1.0073 amu

First, we convert to kilogram

Mass = 1.0073 * 1.66054 * 10^-27 kg

Then we convert to grams

Mass = 1.0073 * 1.66054 * 10^-27 * 10³ g

Mass = 1.0073 * 1.66054 * 10^-24 g

Mass = 1.673 * 10^-24 g

Then we calculate the volume of the proton

Volume = 4/3πR³ where R = Radius

And R = ½d.

First calculate the radius in centimetres

R = ½ * 1.73 * 10^-15 m

R = 0.865 * 10^-15

Convert to centimetres

R = 0.865 * 10^-15 * 10² m

R = 0.865 * 10^-13 cm

So, Volume = 4/3 * 3.14 * (0.865 * 10^-13) ³

Volume = 4.187 * (0.865 * 10^-13) ³

V = 4.187 * 0.865³ * 10^-39

V = 2.71 * 10^-39cm³

So, density = Mass / Volume becomes

Density = 1.673 * 10^-24 g / 2.71 * 10^-39cm³

Density = 0.617 * 10^15 g/cm³

Density = 6.17 * 10^14 g/cm³