00:01
So here in this question we have to draw a photon dispersion curve with the related to a one dimensional monotonic chain where n is equals to 5 of atoms labeled to the valid state in the dispersion curve here.
00:13
So here the atoms are assumed to be connected via massless string of the spring constant.
00:18
Let's say spring constant is beta from here and the distance between the atom in the equilibrium is equals to a.
00:29
So the mass of the each atom let's say is equals to m.
00:32
K or q is a proportional vector and omega is the angular velocity of the wave.
00:37
So we can say that omega from here is equals to under root 4 of beta which is divided by m multiplied by the sin of k of a which is divided by 2.
00:46
That from here is equals to 2 divided by a multiplied by the vs multiplied by the mod of sin of k of a which is divided by 2.
00:54
So the diagram dispersion related to the one dimension of the monotonic lattice will be somewhat like this.
01:00
Let's say we are considering this as a k axis.
01:04
So this is a term from here.
01:05
Let's say this is the central point.
01:07
Let's say this is point o.
01:09
So this will be like say this is our diagram.
01:13
So this is a diagram from here.
01:16
Let's say we are considering this is representing omega and let's say this from here is the first.
01:21
This is a this from here is a first brilliant zone.
01:29
This is the first brilliant zone.
01:32
This is the omega and let's say this is the value from here.
01:36
So this is given from here...