# Help with theoretical density

Gold Member
I posted this in the engineering section but no replies : ( ... Let us see if the physicists can help.

## Homework Statement

Given: Density (D) of Si is 2.328 g/cm^3. Si has diamond crystal structure.
Find: Theoretical density of a single crystal of Si.

## Homework Equations

Theoretical density = m/V

## The Attempt at a Solution

I know mass = (number of atoms) x (mass of atom), in a diamond crystal structure there are: [(1/8) x 8] + [(1/2) x 6] + [(1) x 4] = 8 Si atoms/crystal structure

Now calculating volume is my issue, do I need the lattice constant? If so, how does one calculate it?

Or is it just V = (m x 8)/D = (m x 8)/2.328, where m = 28.1 amu converted to grams?
However, if I do that, I think I'll end up with the given density. What is the difference between the given density and theoretical density? Please help.

Thank you.

## Answers and Replies

Science Advisor
Homework Helper
What is the difference between the given density and theoretical density?
If the theory is very good - nothing. (Usually the "given" density will be some empirically determined value.)

For the lattice constant: what is the Si-Si bond length?

Gold Member
If the theory is very good - nothing. (Usually the "given" density will be some empirically determined value.)
Hmm, that makes sense. Thank you for clearing that out.

For the lattice constant: what is the Si-Si bond length?

Well using google the lattice constant for silicon is 5.43095 Angstroms at 300K. Should this constant be given in the problem? So the volume would be (5.43095 * 10^-8)^3 cm^3 ?

Science Advisor
Homework Helper
That is what it means all right.

Just looking up the lattice constant is a valid alternative to applying some theory to predict it ;)

Gold Member
Haha. Thank you. Finally, someone was able to help me out.