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in this quiz we're looking at the solid state 
structure and it's really going to focus on the

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unit cell and the first question is asking about 
why the unit cell what does it mean to have the

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unit cell do we miss out on things with the unit 
cell and this is really just a definition question

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but is really really important to understanding 
solid state structure as we look at it the unit

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cell is the smallest repeatable unit and so 
remember that solids are kind of like tile

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work in a way where we have a unit that just 
repeats and repeats and repeats has structure

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and it's a consistent structure throughout the 
lattice and if we look at tile work for example

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maybe it's triangle tiles maybe it's square tiles 
but if you zoom in to a certain small perview you

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can see the whole pattern that is really just 
going to repeat itself over and over and that's

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what we have here for Solid State chemistry and 
the unit cell is the smallest possible unit that

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contains all of the structural information and 
as such then we don't miss out on any information

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and if there's some sort of other structural 
element that's included that we didn't capture

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in what we're considering the unit cell well we 
actually just don't have the unit cell yet we

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need to define a larger unit cell that's going to 
capture that information and as such the unit cell

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will contain a different number of atoms depending 
on the complexity of the structure okay one of the

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types of unit cell that is very common to look 
at is called a body centered cubic unit cell

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and here's an image of the body centered cubic 
structure structure uh that's also included so

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the first question is how many atoms are within 
the body centered cubic cell and it's important

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to know the definition of the body centered cubic 
cell where we have eight atoms that are located on

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the corner of a cubic cell right it is H you know 
descriptive it's a cube and there's an atom on

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every corner but there's also an atom that's stuck 
in the center of the body centered cubic cell and

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with that in mind we can consider how many atoms 
are actually there because what you might notice

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is that the corner atoms are not completely with 
within this square unit cell within the cubic unit

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cell rather it's also inside of neighboring unit 
cells but 1/8 of each corner is in the cell and if

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you were to draw these out what you'll see is that 
Each corner atom is actually occupying eight unit

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cells right it's kind of like four on the bottom 
four on top and therefore for eight Corner atoms

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that are within this cell only one8 of each is 
part of this specific cell and therefore it's

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only one corner atom that's contained in the cell 
because each one only has a slice there is also

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the body centered atom and that one completely 
belongs to this cell it's in the center of the

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cell and it's completely within this cubic cell 
definition so that means that there is one body

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centered atom that's inside of the cell this means 
that there's two atoms within the body centered

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cubic unit cell and that's a really important 
thing to keep in mind for considering anything

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about density or unit cell volume or anything like 
that moving forward okay now let's think about

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another body centered cubic unit cell so this is 
tungsten remember this is BCC body centered cubic

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and we'll have that structure we just looked at 
and here you're given the information that the

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unit cell Edge length is 3165 angstroms and the 
goal is to calculate the volume of the unit cell

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in cubic centimeters now one of the things about 
this Solid State chemistry is that a lot of these

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problems are simply geometry we've said that the 
cell has a certain Edge length and all we need

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to know is the volume of this cell and then 
it's a cube so first let's translate The Edge

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length into centimeters because we want to get 
the cubic volume in terms of centimeters cubed

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and we know that the volume of a cubic unit cell 
is just going to be the length cubed right length

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time width time height it's a cube they're all the 
same and so we end up getting this volume in cubic

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centimeters for the unit cell all right with the 
density 19.3 gram per cubic centimeter the goal is

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to calculate the average mass of a single atom of 
tungsten and so here we need to rely on the fact

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we've already calculated the unit cell volume 
the unit cell volume has a volume of 3.17 * 10

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-23 cubic cm and based on this right we know the 
density is a certain number of GRS per cubic cimer

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we know the volume that we're looking at so we 
can simply use our density formula or conversion

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to get the mass within this unit cell and that's 
going to be 6.12 * 10 -22 G pretty small amount

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but this is on the order of just two atoms right 
and that's really important we have to remember

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that this unit cell contains two atoms it's one 
corner atom and one Central atom and so while

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we've gotten the mass of the unit cell if we want 
the mass of just a single tungsten well this is

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the mass of two tungsten it's one unit cell and 
so we need to divide that in half and we get the

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mass of a single tungsten atom to be 3.06 * 10 
-22 G and as a little bonus if we can get the

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mass of one mole of tungsten atoms can we assess 
the quality of how well this calculation has gone

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right it's always good to be able to put things in 
context we know that it's tungsten so if the mass

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of one atom is 3.06 * 10 -22 G how do we get the 
mass of one mole right 3.06 * 10 -22 G per atom

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let's multiply this by the number of atoms per 
mole we're going to cancel out our atoms and get

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a unit of grams per mole 184 grams per mole and so 
this is useful right here's the mass of one mole

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of tungsten it would be 184 grams can we compare 
that to something that we know from the literature

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and the answer is yes right we go to the periodic 
table and we get the molar mass of tungsten 183.0

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G per mole and that's that's pretty close we're 
limited by three significant figures for this

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calculation due to the density of tungsten only 
having three for the given information and within

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significant figures that is in agreement with the 
molar mass of tungsten from the periodic table
