# Desnity and Distibution

1. Apr 19, 2008

### TFM

[SOLVED] Desnity and Distibution

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

Not Sure

3. The attempt at a solution

Any advice would be greatly appreciated,

TFM

2. Apr 19, 2008

### Hootenanny

Staff Emeritus
Hi TFM,

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

3. Apr 19, 2008

### 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

4. Apr 19, 2008

### Hootenanny

Staff Emeritus
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.

Last edited: Apr 19, 2008
5. Apr 19, 2008

### TFM

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

TFM

6. Apr 19, 2008

### Hootenanny

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

7. Apr 19, 2008

### 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

8. Apr 19, 2008

### Hootenanny

Staff Emeritus
Spot on, but watch your units

9. Apr 19, 2008

### TFM

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

TFM

10. Apr 19, 2008

### Hootenanny

Staff Emeritus
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.

Last edited: Apr 19, 2008
11. Apr 19, 2008

### TFM

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

TFM

12. Apr 19, 2008

### Hootenanny

Staff Emeritus

13. Apr 19, 2008

### TFM

Thanks foy all your assistance, Hootenanny

TFM

14. Apr 19, 2008

### Hootenanny

Staff Emeritus
It was a pleasure TFM

15. Apr 19, 2008

### 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.

16. Apr 19, 2008

### Hootenanny

Staff Emeritus
Indeed it is, I assumed that TFM would have realised that.