186k views
1 vote
What is the mathematical relationship between the atomic radius (r) and the lattice parameter (a0) in the BCC structure? a. b. c.

2 Answers

4 votes

Answer

Wrong Category

Explanation:

Dear

Please ask this question in the chemistry section to get the answer

Regards

User Guildner
by
7.8k points
3 votes

Answer: Lattice parameter, a = (4R)/(√3)

Step-by-step explanation:

The typical arrangement of atoms in a unit cell of BCC is shown in the first attachment.

The second attachment shows how to obtain the value of the diagonal of the base of the unit cell.

If the diagonal of the base of the unit cell = x

(a^2) + (a^2) = (x^2)

x = a(√2)

Then, diagonal across the unit cell (a cube) makes a right angled triangle with one side of the unit cell & the diagonal on the base of the unit cell.

Let the diagonal across the cube be y

Pythagoras theorem,

(a^2) + ((a(√2))^2) = (y^2)

(a^2) + 2(a^2) = (y^2) = 3(a^2)

y = a√3

But the diagonal through the cube = 4R (evident from the image in the first attachment)

y = 4R = a√3

a = (4R)/(√3)

QED!!!

What is the mathematical relationship between the atomic radius (r) and the lattice-example-1
What is the mathematical relationship between the atomic radius (r) and the lattice-example-2
User Fan Jin
by
6.6k points