Calculating Particle Distance from Density and Number

[TFM]

[SOLVED] Desnity and Distibution

Homework Statement

I need to calculate the distance between particles. I know the density, and I know how many particles there are, but I am not sure how to calculate the distance between them.

Homework Equations

Not Sure

The Attempt at a Solution

Any advice would be greatly appreciated,

TFM

 

[Hootenanny]

Hi TFM,

Could you please post the full question verbatim, as it is in your textbook/homework sheet.

 

[TFM]

Assume that the sun is made of pure Hydrogen, and take the Hydrogen mass ass being 1.67x10^-27 kg. If the mean mass density of the sun is 1400 kg/m^3, what is the mean number density.

I have calculated this to be 8.4 x 10^29 atoms per cubic meter

hence estimate the typical inter-particle distance

TFM

 

[Hootenanny]

So you know that in one meter there is 8.4 x 10^29 hydrogen atoms. So what volume does each atom occupy? Next, assume that each hydrogen atom is a particle at the centre of a sphere.

 

[TFM]

Each Hydrogen Atom will occupy a volume of $$\frac{1}{8.4X10^{29}}$$ which is $$1.19 x 10^{-30}$$ metres cubed

TFM

 

[Hootenanny]

Each Hydrogen Atom will occupy a volume of $$\frac{1}{8.4X10^{29}}$$ which is $$1.19 x 10^{-30}$$ metres cubed

TFM

Correct, so what is the radius of the sphere with such a volume?

 

[TFM]

Volume of a sphere: $$Vol = \frac{4}{3}\pi r^{3}$$

So $$1.19x10^{-30} = \frac{4}{3} \pi r^{3}$$

so the radius is $$r = \sqrt[3]{\frac{3*Vol}{4* \pi }}$$

Giving the radius: $$\sqrt[3]{2.84*10^{-31}}$$ = 6.57*10^-11 metres Cubed

TFM

 

[Hootenanny]

Volume of a sphere: $$Vol = \frac{4}{3}\pi r^{3}$$

So $$1.19x10^{-30} = \frac{4}{3} \pi r^{3}$$

so the radius is $$r = \sqrt[3]{\frac{3*Vol}{4* \pi }}$$

Giving the radius: $$\sqrt[3]{2.84*10^{-31}}$$ = 6.57*10^-11 metres Cubed

TFM

Spot on, but watch your units

 

[TFM]

Do I now just have to take away the radius of a Hydrogen Atom?

TFM

 

[Hootenanny]

Do I now just have to take away the radius of a Hydrogen Atom?

TFM

Personally, I would have left the answer as it is since once you get down to such small distances the concept of classical radii doesn't really apply. However, you could put both answers to be safe, it depends very much on what your tutor wants.

 

[TFM]

Well, the question then asks you to compareit to the radius of a Hydrogen Atom and a Hydrogen Nuclei.

TFM

 

[Hootenanny]

Well, the question then asks you to compareit to the radius of a Hydrogen Atom and a Hydrogen Nuclei.

TFM

Then I definitely would subtract the hydrogen radius from your answer.

 

[TFM]

Thanks foy all your assistance, Hootenanny

TFM

 

[Hootenanny]

Thanks foy all your assistance, Hootenanny

TFM

It was a pleasure TFM

 

[kamerling]

Is the typical distance between 2 atoms not twice the radius of this sphere? First from one atom to where the spheres meet, then to the other atom.

 

[Hootenanny]

Is the typical distance between 2 atoms not twice the radius of this sphere? First from one atom to where the spheres meet, then to the other atom.

Indeed it is, I assumed that TFM would have realized that.