- #1

mrcake

- 3

- 1

- Homework Statement
- 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 x 10^-27 kg. Determine the density of the proton

- Relevant Equations
- D = m/V

First of all i want is to check if my answer is right or not because i am really not sure about my answer.

Because the length is given in the form of a diameter we will divide that by 2 so we get it in the form of radius,

2.4fm / 2 = 1.2fm = r

Then we will convert the radius from "fm" to "m" so we that'll be,

r = 1.2 x 10^-15 m.

so we now have the radius in meters and from that we can calculate the volume of the proton, by the following formula V = 4/3 x pi x r^3

V = 4/3 x pi x (1.2 x 10^-15)^3 = 7.23 x 10^-45 m^3

Since we have the mass and we calculated the volume we can plug them into formula of density so we'll get,

D = m/V

D = 1.67 x 10^-27 / 7.23 x 10^-45 = 2.3 x 10^17 kg/m^3

Because the length is given in the form of a diameter we will divide that by 2 so we get it in the form of radius,

2.4fm / 2 = 1.2fm = r

Then we will convert the radius from "fm" to "m" so we that'll be,

r = 1.2 x 10^-15 m.

so we now have the radius in meters and from that we can calculate the volume of the proton, by the following formula V = 4/3 x pi x r^3

V = 4/3 x pi x (1.2 x 10^-15)^3 = 7.23 x 10^-45 m^3

Since we have the mass and we calculated the volume we can plug them into formula of density so we'll get,

D = m/V

D = 1.67 x 10^-27 / 7.23 x 10^-45 = 2.3 x 10^17 kg/m^3