Finding the density of a hydrogen proton

In summary, the conversation discusses determining the density of a proton, given its diameter and mass. The formula used is D = m/v, where D is density, m is mass, and v is volume. The mistake of using the diameter instead of the radius is pointed out, and the correct answer is determined to be 5.79058358e-44 meter^3.
  • #1
AryRezvani
67
0

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 1.67e-27 kg. Determine the density of the proton.

Homework Equations



As far as I know, the only required formula is D = m/v

The Attempt at a Solution



Well my attempt looks like this:

(2.4)^3*pi*(4/3) = 57.90583579 fm^3

Used google to convert that into kilometers, and got 57.905835791 (femtometer^3) = 5.79058358e-44 meter^3.

Divided 1.67e-27 kg by 5.79058358e-44 meter^3.

Got 2.883992566e16 but apparently, it's wrong.

Any suggestions guys?
 
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  • #2
Hello, AryRezvani.

Note they give you the diameter, not the radius of the proton.
 
  • #3
TSny said:
Hello, AryRezvani.

Note they give you the diameter, not the radius of the proton.

Ahh... Feeling rather stupid now.

Thanks.
 
  • #4
That's not stupid, just a little oversight...(I'm doing things like that a lot in my old age :redface:).
 
  • #5


Your attempt at solving for the density of a hydrogen proton is on the right track, but there are a few things that can be improved upon.

First, let's review the formula for density: D = m/v, where D is density, m is mass, and v is volume. In this case, we are given the mass of the proton (1.67e-27 kg) and we can calculate the volume using the given diameter (2.4 fm). However, we need to convert the diameter from femtometers to meters in order to use the formula.

To convert femtometers to meters, we can use the conversion factor 1 fm = 1e-15 m. So, the diameter of the proton in meters would be 2.4e-15 m.

Next, we can calculate the volume using the formula for the volume of a sphere: V = (4/3)*pi*r^3, where V is volume and r is the radius. In this case, the radius is half of the diameter, so r = 1.2e-15 m. Plugging in these values, we get V = (4/3)*pi*(1.2e-15)^3 = 7.238229473e-46 m^3.

Now, we can plug in the values for mass and volume into the density formula: D = 1.67e-27 kg / 7.238229473e-46 m^3 = 2.307e19 kg/m^3.

So, the density of a hydrogen proton is approximately 2.307e19 kg/m^3.

I hope this helps and clarifies any confusion. Keep up the good work!
 

1. What is the definition of density?

Density is a measure of the amount of mass per unit of volume. In other words, it tells us how tightly packed the particles of a substance are.

2. How do you find the density of a hydrogen proton?

The density of a hydrogen proton can be found by dividing its mass by its volume. The mass of a hydrogen proton is approximately 1.67 x 10^-27 kilograms, and its volume is incredibly small, so the resulting density is extremely high.

3. What is the mass of a hydrogen proton?

The mass of a hydrogen proton is approximately 1.67 x 10^-27 kilograms. This is an incredibly small mass, as protons are subatomic particles.

4. How do you measure the volume of a hydrogen proton?

The volume of a hydrogen proton is incredibly small and cannot be measured directly. Instead, its volume can be calculated by using the known radius of a proton (approximately 8.41 x 10^-16 meters) and using the formula for the volume of a sphere (4/3πr^3).

5. Why is it important to find the density of a hydrogen proton?

Knowing the density of a hydrogen proton is important for understanding the behavior and properties of matter at a subatomic level. It also helps us to understand the physical constants and laws that govern our universe.

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