# Desnity and Distibution

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.

Not Sure

## The Attempt at a Solution

Any advice would be greatly appreciated,

TFM

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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

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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.

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

TFM

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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

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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

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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.

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

TFM

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

TFM

TFM
Thanks foy all your assistance, Hootenanny

TFM

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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.

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