Calculations Involving Unit Cell Dimensions Video Lecture - NEET

hello friends this video on solid sales
part 18 is brought to you by exam feel
calm no more fear from exam now let's
suppose we change the question we are
are we asked you to find the dimensions
of this unit cell
this is unit cell and you are asked to
find a dimension of this unit cell what
is the length you are been given other
parameters like what is the unit cell
type whether it is a body centered face
center and you also been told the molar
mass the molecular mass of this compound
density is also given so in that gives
how will you find the unit cell
dimension correct so actually from the
unit cell dimension you can actually
find the volume of the unit cell correct
and if you know density of the metal can
calculate the mass C from dimension what
we can find volume and density is equal
to mass by volume so if density is given
volume is going you upon the mass if
density if mass is giving you find the
volume and volume from volume you can
find by making reverse engineering
correct but desti mass and volume is
linked and just assume volume has
nothing but a Q right this is the length
cube so dimension Q so using these we
can actually find the density or you can
find the mass or we can find the
dimension so let us derive the
relationship between this right it is a
very accurate method Ashley so by
actually diffraction this found at the
length of the unit cell crystal is a
let's suppose we have found that using
actually fraction so we know that this
is the or let's first find the formula
right we told that density is equal to
mass per volume so let's focus on one
cell one self
so in one cell we can have the number of
atoms we have seen that in body
excellent it is 1 in face centered it is
4 in sorry
in the normal 1 it is 1 in the face
Center it is 4 and bodies and it is 2
right
this is body central VA center it is a
normal one
normal cubic structure you close to back
now this number is very so let me give a
name to enter this area that will
nothing but the number of atoms in the
valley so for a given cube let's do a
general formula density is what P is
equal to mass what is the mass mass is
what the number of atoms you have into
the mass of one atom so what is the
number of atom number of atom is Z here
Y is then because we are doing a general
formula if it is C CB will put DES equal
to 1 BC C is equal to 2 FC C is equal to
4 like that that into mass of one atom
so mass of one matter nothing but my
molar mass by Avogadro number na because
one mole one mole is equal to six point
zero 2 2 into 10 to the power 23 atoms
no and one mole is some gram right
depending on what compound is written
for example hydrogen is one gram like
that so that is not going to molar mass
so if you want to find the weight of one
atom that will be nothing but the molar
mass by
number correct this is my total mass of
all the atoms in a given Q now by volume
is what my volume of unit cell correct
so what is the volume of unit cell is
nothing but a cube if a is my edge this
is my formula density is equal to mass
by volume ma has nothing but Z that is
nothing but my number there is based on
the type of packing into mass of one
atom that is nothing but molar mass by a
vector number divided by volume of unit
cell that is a cube it is a formula M
derive okay and this is a very very
critical formula
please remember density is equal to Z M
by n a two-week this is a very very
critical point and with this formula
actually we can find the value of n a
also if we know the density of a
substance if we know the Z by the x-ray
defraction obviously you'll know the
type of packing it is more room as we
know and by x-ray diffraction find the
value of a we can find the value of n a
also right so any unknown you have one
two three four five values right it is
the relationship between these five
values so you know the value of for
thing you can easily find the first are
correct so we'll take some numerical on
that so the question is an element is a
body centered cubic structure
so let's first draw a body centered
agree stops the edge of 288 Pico meter
that is my length of a 288 Pico meter
this is my n the density of element is
7.2 gram per centimeter cube density is
7.2 gram per centimeter cube right the
question is how many atoms are present
in to 0-8 gram of the Elementor
that is the question see density is what
mass by volume mass is something I know
right this is something I know and
density or something which I know so I
can actually find the volume of my 208
grams arable correct if I can find the
volume of this I can find the number of
cells easily got this volume which I get
is nothing but my volume of cells unit
cells correct so here I'm not I'm not
talking about one atom I'm talking
before you one a little there n namibian
sir so you will get volume of n number
of in itself and I know that the volume
of one unit cell is a cube a I know so
with that I can find the number of unit
cells open the 10 what I'm trying to say
see there are 200 grams of element so I
with that I can find them volume of this
200 grams of element will have n number
of in it cells correct so let's find
that first so volume of 200 8 grams of
element is equal to mass by density mass
is what 200 gram and this is density is
7.2 gram or centimeter view please note
the are SI units the units here so here
everything is gram so I just I didn't
convert into SI unit so gram and graph
cancel with that you get twenty eight
point eight eight in centimeter cube
will come up centimeter cube this is the
volume of 200
eight grams of element it will have it
will have n number of cells here itself
correct so let's find the volume of one
unit cell volume of V one in itself so
since it is in centimeter cube let's
find in centimeter cube only and that is
nothing but a cube is 288 Pico meter so
let us convert this into centimeter
correct
so 288 Pico meter is nothing but 288
into 10 to the power minus 10 centimeter
correct so you just solve this 288 into
10 to the power minus 10 centimeter
whole cube what you get is 2.3 9 into 10
to the power minus 23 centimeter cube
this is the volume of one unit cell so
if I have to find the number in itself
number of unit cells there is nothing
but total volume total volume of unit
cells correct by a volume of one unit
cell so all the volume of unit cell is
given here to eight point eight eight
same to inter to divide by volume over
unit cell that is two point three nine
into ten to power minus 23 centimeter
view please note is all same units
cancel and with this you saw you get
answer as
one point two zero eight into ten to
power 23 unit cells so 280 grams of
element will have these many unit cells
but the question is different question
is how many atoms are there now we'll
take the advantage of the fact that it
is body centered cubic structure since
it is body centered unit structure each
unit cell will have two atoms so number
of adders will be how much you multiply
this thing by two so let me write it
here number of atoms will be what two
into this number twelve point zero 8
into 10 to the power 23 you solve this
you get 24 point 1 6 into 10 to the
power 23 atoms and that is principle
pretty easy
so from 208 grams of the element we
found that what is the total volume and
we know that 1 unit cell has this much
volume total your number of units of the
form want to find total number of atoms
1 unit cell has two atoms total number
of atom is 2 into this valve that is 24
point 1 6 into 10 to the power 23 thank
you visit exam viacom to watch more
videos Atem free online test get 3 study
materials find tutors and mentors and
much more thanks once again