Packing Fraction Calculation - Solid State Video Lecture | Physical Chemistry

we have to calculate packing fraction
packing fraction DHEC you have me a
lotta luck packing here ll always say
spares karinski are those missus subset
other space cone utilize Karina tiger on
policy CPA HCP simply well as either
face centered cubic o DK so if you focus
off on right angle triangle a B C so
what you come to know that AC square
isn't a thing but a d square plus BC
square AC square is actually not up
dickhead so you have take half our hair
is hollow sphere can be half R or s
philosphy kadai two are so in total it
is 4 R square is equal to a square plus
a square a cuticle your ad hand or DC
and those all are edges of the unit cell
tomorrow ahead
solving this what we come to know that a
is nothing but 2 under root two are a
began packing fraction McAllen the
volume occupied by force fair queuing
cookie face centered in sandwich are
spare hotel per unit cell child items of
the hand
alright of spherical hazardous for into
a Kaval young kitten ahead 4 by 3 PI R
cube with exosphere divided by a cube
and a is 2 under root 2 R cube in 200
and when you solve it this comes out to
be a 74% so 74% of the spaces of Q is
utilized here it's candor
next is our a body centered cubic it's
Megara big a triangle up triangle T key
f e d skinner of dingy so we have FD
square is equal to f e square plus e be
square or
jo f e here that is nothing but again
each of the unit cell similarly e days
each of them
this comes out to be 2 a square I
chopped up now just focus on a
right-angled triangle B E
a bisque in a cha we have two triangles
one triangle is B is it be known
I'll be scan that we have two triangles
first is triangle a F the in fact ADF
it's a right angle triangle or eskender
what we have in a F square is equal to a
B square plus B F square a F is nothing
but a my path ie FS for our square again
Q to get this is art this is 2i and this
is again so it's for our ad is what ie a
square plus B F on a putana here what is
the F square it is a square Q key ad
square is a square cookie
II D is nothing but age land ticket to
make our triangle Mirjana hoga let's
have a look at triangle a B okay let's
have a triangle let's have a look at the
triangle F it's e F the EFD it's kind of
what you come to know that FB ad b f
square is equal to f e square plus e d
square this is a square plus a square
because they don't know we can age
length here or it comes to be to a
square so nice ever that really IDF is
nothing but 2 f square good
Tomica karna here I'm a Latina here sk
according when we solve a we just put
the value what we come to know that for
our whole square is equal to a square
plus we have what - a
Square take it then we solve it what we
can't
okay let's solve it it would be 16 R
square is equal to 3a squared or when we
go for the value of a it would be 16 by
3 R square bull and in the room this
comes to be 4 upon the root 3 ah ok now
putting this these all values they came
body centered cubic in here these are
not for sphere these are body centered
killing 2 sphere so it would be packing
fraction would be 2 into X where K
volume 4 by 3 PI R cube a cube is Omni
gesture we calculate kita y is nothing
but it is 4 by root 3 I cube in 200
solving this we get it like 68% next is
simple cubic is gonna be tension in a
and there there's only one sphere most
one spherical volume is 4 by 3 PI R cube
total volume is a cube and for this edge
length is nothing but 2 R half are from
here half are from but not from here 1
are from here it would be like 2 R cube
in 200 job we see him solve Carini we
will get it like 52.4% to the subsidy of
the packing efficiency here that is for
our face centered cubic
the next is calculations involving
dimension of a unit cell
let's see which is density in economy
here each unit cell key to density a
formula cava obviously mass upon volume
that is mass of unit cell divided by
volume of unit cell a mass of unit cell
yoga that would be equal to number of
atoms per unit cell into molar mass
thicker it is molar mass of every item
divided by volume of unit cell is a cube
the key and 2 molar mass for guiana
tomato egg volume egg was commercially a
katenka so we have to divide it by I
will get drawn number take a to your
density who are net is dead upon MW that
is molecular weight divided by a cube
into and a so this is the formula used
for calculation of density of a unit
cell
every density given here to find out our
molar mass of an atom or molar mass or
density given head to find out
age of the unit cell this is very
important formula or a exam may access a
time TK