A proton, which is the nucleus of a hydrogen atom, can be modeled as a sphere with a diameter of 2.4 fm and a mass of 1.67 10-27

Question

lara [203]

3 years ago

12

A proton, which is the nucleus of a hydrogen atom, can be modeled as a sphere with a diameter of 2.4 fm and a mass of 1.67 10-27

kg. Determine the density of the proton.

Physics

2 answers:

Step2247 [10] · Answer 1 · 2021-11-18T09:33:33+03:00

For the answer to the question above asking to d<span>etermine the density of the proton.
</span>Density is mass over volume.

The volume of a sphere is 4πr³/3. r is half the diameter.

So the density would be 2.3×10¹⁷ kg/m³.
I hope my answer helped you. Feel free to ask more questions. Have a nice day!

mr_godi [17] · Answer 2 · 2021-11-18T10:55:22+03:00

<h3>The density of the proton is 2.3 x 10²⁰ g/m³.</h3><h3 /><h3>FURTHER EXPLANATION</h3>

The density of a substance is equal to the ratio of its mass and volume.

$Density = \frac{Mass}{Volume}$

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.

<u>STEP 1:</u> To determine the volume, the equation for the volume of a sphere must be known.

$V \ = \frac{4 \pi r^{3}}{3}\\$

where r is 1/2 the diameter of the sphere.

Plugging in the values to get the volume in cubic meters:

$V \ = \frac{4 \pi (1.2 \times 10^{-15} \ m)^3}{3}\\\\\\\\boxed {V = 7.23456 \times 10^{-45} \ m^3\\}$

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.

$Density \ = 1.67 \times 10^{-27} \ kg \times \frac{1000 \ g}{1 \ kg} \times \frac{1}{7.23456 \times 10^{-45} \ m^3}\\\\\\\boxed {Density \ = 2.3084 \times 10^{20} \frac{g}{m^3}\\}$