00:01
First of all, we have to find out here edge length of the cubic crystal we have given.
00:06
Okay, and with the help of that we will find out the atomic radius.
00:10
So we know that since density of crystal, so that is we have z multiplied by m divided by n, n, a, cube.
00:36
So here z is the number of atoms per unit cell.
00:42
M is the atomic mass of that metal or substance which is it is made up of, okay? and n, e that is the avogadro number and a cube.
00:54
So that is the here the cubic volume we have.
00:59
Okay.
01:01
So now here this density of crystal can also be represented as d.
01:07
So we can find out here a cube that's equal to z multiplied by m divided by n a multiplied by d.
01:16
Okay.
01:18
So now putting the values.
01:20
So for bcc that is body centered cubic unit cell.
01:28
So z number of items per unit cell that is two.
01:33
Okay.
01:34
So putting this value.
01:36
So we have a cube is equal to 2 multiplied by m 50 .9 gram per mole divided by we have na that is we have 6 .022 multiplying 10 raise to power 23 and this will be mole inverse here.
02:08
Okay and this can also be written as gram mole inverse and multiplied by we have density that 5 .96 gram per centimeter cube okay so now solving this this will be 101 .8 divided by this is 35 .89 and now this can be written as multiplied by 10 raised to power 23 okay and the final unit so that will be centimeter cube okay so a cube that's equal to 2 .836 multiplying 10 raised to power minus 23 okay this power when goes to numerator side becomes negative and this will be in centimeter cube and now shifting the decimal so a cube that's equal to 28 .36 multiplying 10 raise to power minus 24 centimeter cube okay and now here we have cube on this left side so we have to solve cube root for this so this will be a and now cube root of 28 .36 multiplying 10 raise to power minus 24 centimeter cube.
03:59
So this will be a is equals to.
04:03
So this will be 3 .049 multiplying 10 raise to power and solving the power...