Question

Potassium metal crystallizes in bcc lattice. The edge length of unit cell is 4.3 A0

. Find the

radius of potassium atom.​

Answer 1

Given:

Potassium metal crystallizes in bcc lattice. The edge length of unit cell is 4.3 A°.

To find:

Radius of Potassium atom.

Calculation:

First of all , kindly look at the attached diagram to understand the disposition of various atoms in a BCC lattice.

Now , for competitive exams , always remember the following expression relating age length and radius of an atom in this lattice:

$\boxed{ \sf{4(radius) = \sqrt{3} (edge \: length)}}$

• This equation can be easily proved using Pythagora's theorem

Now , putting the values:

$= > \sf{4(radius) = \sqrt{3} \times 4.3}$

$= > \sf{radius = \dfrac{\sqrt{3} \times 4.3}{4}}$

$= > \sf{radius = \dfrac{7.44}{4}}$

$= > \sf{radius = 1.86 \: {A}^{ \circ} }$

So, radius of Potassium atom is 1.86 A°.

Hope It Helps.