Determining the density of Silicon

[weston_sagle]

Homework Statement

There are 8 atoms in a unit cell of Si. Silicon has an atomic weight of 28.09 and a lattice constant equal to 5.43 A. Determine the density of silicon/

Homework Equations

?

The Attempt at a Solution

?

 

[weston_sagle]

Figured it out.
5.43 is in angstroms, which is 10^-8 cm.
So density is atoms for cm^3

so 8/(5.43x10^-8)^3 = 4.99x10^22/cm^3

Simple as that.

 

[tomcue]

To determine the density of silicon, we need to use the formula for density, which is mass divided by volume. In this case, the mass will be equal to the atomic weight of silicon (28.09 g/mol) multiplied by the number of atoms in a unit cell (8). The volume can be calculated by multiplying the lattice constant (5.43 A) by itself three times (since we are dealing with a three-dimensional structure). This gives us a volume of 157.7 A^3.

Therefore, the density of silicon can be calculated as follows:

Density = (28.09 g/mol * 8 atoms) / (157.7 A^3) = 1.42 g/A^3

This means that the density of silicon is 1.42 grams per cubic Angstrom (A^3). This is a very small unit of measurement, so it is more common to express the density of silicon in units of grams per cubic centimeter (g/cm^3).

To convert from A^3 to cm^3, we can use the conversion factor of 1 A^3 = 10^-24 cm^3. Therefore, the density of silicon can also be expressed as 1.42 * 10^-24 g/cm^3.

In conclusion, the density of silicon is approximately 1.42 g/A^3 or 1.42 * 10^-24 g/cm^3. This is a very important value to know in the field of materials science and engineering, as it is a key property in determining the behavior and properties of silicon in various applications.