Primitive Unit Cell (Simple Cubic) Video Lecture - JEE

welcome to Elektra line and now we're
going to talk about the crystal
structure of atoms when they're in a
solid state so now we're taking a look
at the solid portion of chemistry here
and what we'll find out is that when
atoms and ions and molecules come
together and set themselves up in a
solid state so that they're hooked
together and they don't move relative to
each other while they may they may
vibrate of course through thermal action
but they're no longer moving relative to
each other they're staying put in place
we can try to figure out what the
structure of those atoms and those ions
are now we're going to run through
different types of structures one of the
most common one is what we call the
simple cubic structure and there's
different types of atom and ion build up
so to speak within those structures but
the general structure is that they're
they're cubic in shape there's perfect
symmetry in such a way that the width
the length and the height of the cube is
exactly the same for example a equals B
equals C so let's go ahead and write
that a equals B equals C of a simple
cubic structure and also that the angles
are all 90-degree angles so the face is
relative to each other are at 90 degrees
from each other so we could say that the
angle alpha is equal to angle beta is
equal to the angle gamma is equal to 90
degrees so we have a perfect cubic
structure and so for example atoms may
be packed together like this and the way
we draw the cubic structure is by
putting the corners of the cube at the
center of the atoms in such a way that
no matter where you put this cube the
content of the cube will be exactly the
same so if we draw another cube right
next to it with with four more these
atoms there you can see that the next
cube will look exactly the same as this
cube will exact same as the one to the
left to the top to the bottom of the
front and back and so forth now of
course not always are the ions the same
shape most of the time they're not
they're different shape and so there may
be a slight different way in which the
atoms are arranged for example in sodium
chloride the chlorine atom the chlorine
ion is much bigger than the sodium ion
so they tend to pack slightly
differently it's still a cubic shape but
you can see in order to draw what we
would call the unit cell the cell that
represents the same everywhere within
the structure has been drawn a little
bit differently
it has to be drawn from the center of
the large chlorine chlorine ion to the
center of the large chlorine ion when
you find it again with the sodium mine
in between notice you'll have a big
chlorine ion in here chlorine there
chlorine there so the unit structure
here is a little bit different than it
is there but again if you take this cube
you place it over here you'll have the
exact same contents of that crystalline
structure over there so that's the
concept of the unit cell so what we're
going to do in the next so many videos
we're going to try and figure out what
is exactly contained within each unit
cell depending upon what the crystalline
structure is what the atoms and ions are
involved in the crystalline structure
trying to figure out how much of each
atom within the structure is part of the
unit cell for example how much if this
particular atom is part of this
particular unit cell and so you may say
well isn't the whole atom part or the
whole ion part that cell no that's not
exactly true because what we're doing
here is put in the corner right at the
center of that atom of course in reality
it's more like this rather than this but
sometimes it's easier to see when we
draw it out like that
now imagine there's going to be a cube
in the front there's going to be a
coupon top to the side and just end at
the bottom right here and it's going to
be underneath to the left of the right
and so forth in such a way that each of
these atoms at each corner is really
shared by eight of these unit cells only
one-eighth of the atom belongs to this
particular unit cell during a 7h belong
to the other seven unit cells that would
be adjacent include note encompassing
part of this particular atom like that
so you can imagine if you draw another
one like here you go straight out this
way you can see that now that this atom
is shared between this one this this
cell and this cell if you then draw one
in the front this way in the front that
way you can see that this atom is also
shared in the unit cell over here and
the unit cell over there so now you have
four unit cells here and so only have
the atom belongs to those four unit
cells they don't have the atom would be
sticking above those four unit cells so
if you then place on top of that another
for these unit cells that half of the
atom would then be subdivided between
those four cells right above it and so
- way that 1/8 of this atom blocks on
each of the eight cubes or unit cells
and come to sing that particular region
so how much of the atoms are then inside
any one of these unit cells in the case
of an arrangement like this one-eighth
of this atom would be in the cell 18.1
one eighth of this one one eighth of
this one one eighth of that one one
eight one eight and then of course this
one in the back here which I didn't draw
if I were to draw that it would kind of
like sit in the back like this around
the corner in the back of the cube and
so you can see there's a total of eight
of those atoms each of them donating or
and come to saying one eighth of that
atom within that unit cell so this
particular arrangement of atoms or ions
would only have one atom within that
particular unit cell as you will see
when we start looking at things such as
sodium chloride which is a little bit
more complicated it's a different way in
which you want to count how much of each
atom belongs to that unit cell and how
you then can find out how many atoms are
contained in a cell in the later video
I'll show you how to do that one thing
to keep in mind is that it's important
to figure out the size of these unit
cells as well for example with sodium
chlorite notice that the radius of the
chlorine ion is about 181 Pico meters
the radius of the sodium mine is about
95 Pico meters so how big is that unit
cell well through x-ray diffraction
techniques we discovered that the unit
cell is actually has a side of 564 Pico
meters now if you imagine for a moment
that you would have to take the full
diameter of the sodium ion and 1/2 a
radius I'm sorry 1/2 a diameter or
radius of this chlorine ion and a radius
of that chlorine ion and add it all
together what would that add up then up
to so here we have 181 picometers for
this one plus twice 95 plus 2 times 95
Pico meters plus then again 181
picometers from that one and let's see I
have a calculator right here let's take
a quick check here 181 times 2 plus 95
times 2 equals that would be total of
552
picometers so from simple calculation
and knowing the average size of these
ions you would expect the unit cell in
this case to be 552 Pico meters on each
side in actuality it's a little bit more
it's 564 Pico meters so why the
difference well it turns out that these
are average values for the radii of
these particular ions depending upon
what they're mixed with that radii can
change that of course it involves
electro electrical forces and so
sometimes they're squeezed a little bit
closer together sometimes they're
repelled out a little bit further out
and in the case of the sodium chloride
chloride notice that the close proximity
of the chlorine ions probably pushing
these ions a little bit further apart so
that the unit cell has an side distance
or length of 564 Pico meters rather than
what we would expect to be 552 but it's
a pretty close agreement so that's the
basics of the unit cell in the crystal
structure of atoms in the solid state
and now we're going to systematically
look at the various types of crystal
structure then it can exist and the
various ways in which atoms are packed
with those crystal structures and from
that we can calculate densities and so
forth and that's a pretty neat thing so
stay tuned take a look at the other
videos if you're interested in this kind
of stuff