Lead has a face-centered cubic lattice with all atoms at lattice points and a unit-cell edge len

Lead has a face-centered cubic lattice with all atoms at...

Key Concepts

Face-Centered Cubic (FCC) Structure

The FCC structure is a type of crystal lattice where atoms are located at each of the corners and the centers of all the faces of a cube. This arrangement leads to a specific number of atoms per unit cell, which is critical for calculating properties such as density. In an FCC lattice, although there are 14 atomic positions, due to sharing between adjacent cells, there are effectively 4 atoms per unit cell.

Unit Cell Volume

The unit cell is the smallest repeating structure in a crystal lattice, and its volume is calculated using the cell edge length. This volume is fundamental when determining the density of a material because it provides the space over which the mass of the atoms in the unit cell is distributed.

Density Calculation in Crystals

Density in the context of a crystal lattice is determined by dividing the total mass of the atoms present in one unit cell by the volume of that unit cell. This requires knowing the effective number of atoms per unit cell, the atomic mass of each atom, and the appropriate unit conversions to ensure consistency.

Atomic Mass and Avogadro's Number

Atomic mass is a measure of the mass of a single atom, usually provided in atomic mass units (amu). Avogadro's number is used to convert the atomic mass of a single atom into the mass corresponding to a mole of atoms, allowing the calculation of the total mass present in a unit cell when multiplied by the effective number of atoms.

Transcript

00:02 Okay, so this question gives us some information about the unicell and asks us to calculate the density.

00:14 So the first piece of information we get is the lat has a face -centered cubic lattice.

00:30 And also what gives us is the edge lens of the unicell, which is 495 picometers.

00:41 Which is around 495 times 10 to minus 12 meters.

00:49 Also, it gives us the mass of the single atom, which is 207 .2 am u, and we can use 207 .2 times 1 .67 times 10 to minus 24.

01:15 And this equals to around 207 .2 times 1 .67.

01:28 It's actually equals to around 346 .024 times 10 to minus 24 grams.

01:40 Grams.

01:42 So this is a mass of the single atom.

01:47 We know for density calculation we can easily gather expression equals to the mass over the volume.

01:59 And here we just use a single unit cell to do the calculation.

02:05 So we know it actually equals to the mass of the cell over the volume of the cell.

02:12 The mass of the cell.

02:13 The mass of the cell.

02:13 The mass of the cell is a single unit of the cell.

02:13 Of the cell equals to the number of the atoms in the cell times the mass of the single atom.

02:22 And the volume of the cell actually equals to the edge lens power 3.

02:27 And now what we need to know is the number of the atoms in the unit cell...

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