The density of a substance is equal to the ratio of its mass and volume.
[tex]Density = \frac{Mass}{Volume}[/tex]
To get the density of the proton, the following steps must be completed:
1. Determine the volume of the spherical proton.
2. Calculate the ratio of the mass and the volume of the proton.
STEP 1: To determine the volume, the equation for the volume of a sphere must be known.
[tex]V \ = \frac{4 \pi r^{3}}{3}\\[/tex]
where r is 1/2 the diameter of the sphere.
Plugging in the values to get the volume in cubic meters:
[tex]V \ = \frac{4 \pi (1.2 \times 10^{-15} \ m)^3}{3}\\\\\\\\boxed {V = 7.23456 \times 10^{-45} \ m^3\\}[/tex]
STEP 2: Once the volume is known, the density can be calculated by getting the ratio of the mass (in grams) and the volume in cubic meters.
[tex]Density \ = 1.67 \times 10^{-27} \ kg \times \frac{1000 \ g}{1 \ kg} \times \frac{1}{7.23456 \times 10^{-45} \ m^3}\\\\\\\boxed {Density \ = 2.3084 \times 10^{20} \frac{g}{m^3}\\}[/tex]
Since the least number of significant figures in the given is 2, the final answer must also only have two significant figures.
Therefore,
[tex]\boxed {\boxed {Density = 2.3 \times 10^{20} \frac{g}{m^3}}} \[/tex]
keywords: unit conversion, dimensional analysis, density
