The density of gold is 1.93E4 kg/m3 and the cell volume is 6.78E-26 L. Determine the number of atoms in the unit cell. Note: the number of atoms in a unit cell is a whole number. For the purposes of this calculation, enter your answer to 3 significant figures.

Thy or Roxanne or ??,

You work this almost like the one I helped you through on the previous post. Gold is a face centered cubic crystal; therefore, there are 4 Au atoms per unit cell. But you are supposed to calculate it. Hint: First determine the mass of 6.022 x 10^23 atoms and from that the mass of 1 Au atom. Then use the density and volume to determine the mass of a unit cell. From there you see if there is 1 or more than 1 unit cell in the mass.

To determine the number of atoms in the unit cell, we need to know the volume of the unit cell and the density of gold. Here's how you can calculate it:

1. Convert the cell volume from liters to cubic meters:
- 6.78E-26 L = 6.78E-29 m³ (Remember, 1 L = 1E-3 m³)

2. Divide the density of gold by its molar mass to find the number of moles per cubic meter:
- Density of gold = 1.93E4 kg/m³
- Molar mass of gold = 196.97 g/mol = 196.97E-3 kg/mol
- Moles per cubic meter = Density / Molar mass
- Moles per cubic meter = 1.93E4 / 196.97E-3

3. Calculate the Avogadro's number:
- Avogadro's number = 6.022E23 atoms/mol (known constant)

4. Multiply the moles per cubic meter by Avogadro's number to find the number of atoms per cubic meter:
- Number of atoms per cubic meter = Moles per cubic meter * Avogadro's number

5. Multiply the number of atoms per cubic meter by the volume of the unit cell to find the number of atoms in the unit cell:
- Number of atoms in the unit cell = Number of atoms per cubic meter * Cell volume

Now, let's calculate it:

Moles per cubic meter = 1.93E4 / 196.97E-3 = 9.812E6 mol/m³

Number of atoms per cubic meter = 9.812E6 * 6.022E23 = 5.909E30 atoms/m³

Number of atoms in the unit cell = 5.909E30 * 6.78E-29 = 4.002E2 = 400 atoms (rounded to 3 significant figures)

Therefore, there are 400 atoms in the unit cell.