Question

silver crystallizes in face centered cubic unit cell. a silver atom is at edge of each lattice point the length of the edge of the unit cell is 0.4086 nm. What is theatomic radius of silver

Answer 1

;

Atomic radius of silver =144.5 pm

(N.B. for questions of this type the calculated answer is usually the same as that found in literature so can be easily checked)

Explanation;

Step 1)

To answer this question first you must know what a face-centered cubic cell looks like;

this is theunit cellwhere to dots represent silver atoms for this question.

Step 2)

As atoms 'touch' diagonally across the face of the cube, as shown above.

There are four radii (r) across the face of the cube. As the diagonal across the cube forms a right-angled triangle with the sides (a), usingPythagoras' theorem (a²+ b²= c²);

∴ a²+ a²= (4r)²

∴ 2a²= 16r²

∴a = r

Step 3)

Asedge of the unit cell (a) is 0.4086 nm.

∴r= 0.4086 nm

∴ r = 0.1445 nm (3sf)

as1 nanometre = 1000 picometres

∴ r = 144.5 pm

Hope this helps!