Question

Question 5
Edge length of unit cell of chromium metal is 287 pm with bec arrangement. The atomic
radius is of the order
{a) 287 pin
(b) 574 pm
fe) 124 27 pm
(d) 143 5 pm​

Answer 1

in bcc unit cell,z=4

relation between a and r is given by

r=√3a/4

r=√3×287/4

r=124.27pm

Answer 2

Answer:

Hence, the correct option is (c) 124.27 pm

Explanation:

What is bcc arrangement?

The unit cell in a body-centered cubic (bcc) arrangement of atoms is made up of one atom in the cube's body center and eight atoms arranged at the cube's four corners. A unit cell in a bcc configuration consists of 2 atoms (8 corner atoms divided by 18) and 1 center atom. The structure is typical for alkali metals and early transition metals, and the packing is more effective (68%) than simple cubic. BCC structures can be found in ferrite, chromium, vanadium, molybdenum, and tungsten metals. These metals are quite strong and not very ductile.

Formula for bcc arrangement:

$\sqrt{3} a = 4r$

$r = \frac{\sqrt{3}a }{4}$

Packing efficiency = $\frac{Volume occupied by particles in unit cell}{Total volume in unit cell}$ x 100

Thus, 68% of the total volume in bcc unit lattice is occupied by atoms and 32 % is empty space or void volume.

The atomic radius is of the order:

$r = \frac{\sqrt{3}a }{4}$

$r = \frac{\sqrt{3} }{4}$ x 287

$r = 124.27 pm$

So, the atomic radius is of the order is 124.27 pm.

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