1) Consider diamond lattice structure with a = 6 Å...

1) Consider diamond lattice structure with $a = 6 \AA$ (angstrom). If Si has 28 g/mol atomic mass a) Calculate Si's mass density (in g/cm³). Calculate electron density in the filled valence band.

Transcript

00:01 So, here we are considering about niobium.

00:03 So, it is given that niobium has a bcc structure and atomic radius is given that is equals to 0 .143 nanometer and then atomic weight is given that is equals to 92 .91 gram per mole.

00:17 So, we have to calculate the theoretical density of the nb.

00:22 So, from here we are considering we are having the value of nb atomic radius is given that is in nanometer we can convert this into meter that become equals to 0 .143 multiplied by 10 raised to the power minus 9 meter weight is in gram per mole.

00:35 So, theoretical density of niobium is given as rho naught n multiplied by the a that is divided by vc which is multiplied by the ma.

00:43 Let's say this is the equation number 1 from here.

00:46 Now we are having bcc lattice and the volume of vcc lattice is given as 4 of r which is divided by under root 3 to its whole cube.

00:55 Here we are having the value of the n that is equals to 2 because in bcc lattice atoms are present in the corners and one in the base.

01:03 So, their collectivity are 2 atom.

01:05 So, the value of na is equals to 6 .023 multiplied by the 10 raised to the power 23 atoms per mole.

01:14 So, we can say that putting all this value in the equation the value of rho naught become equals to 2 which is multiplied by the 92 .91 that is divided by 4 multiplied by the 0 .14 that is multiplied by the 10 raised to the power minus 3 to its whole square which is already divided by under root 3 multiplied by the 6 .023 10 raised to the power 23.

01:33 Solving the term from here we get the value of rho naught that become equals to 8 .565 gram per centimeter cube.

01:40 Hence the answer to the first part of the question.

01:43 Now we are considering about the second part where we are given a indices of the direction.

01:48 So, here in this part we have to sketch the directions which we are given here.

01:55 First is a negative, negative and 1.

02:00 This is the first direction which we need to sketch from here.

02:03 So, we can say that this directions in a cube are represented as let's say this is our unit lattice.

02:12 So, this is our unit lattice.

02:14 This is representing z axis.

02:17 This from here is representing x axis and this from here is representing y axis...

Question

1) Consider diamond lattice structure with $a = 6 \AA$ (angstrom). If Si has 28 g/mol atomic mass a) Calculate Si's mass density (in g/cm³). Calculate electron density in the filled valence band.

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