Question

A metal crystallises with a face centered cubic lattice. If edge length of the unit cell is 400 pm then the radius of the metal atom will be 0 173.2 pm O 346.4 pm O 141.4 pm O 100 pm​

Answer 1

Answer:

For FCC r=

2

2

a

Hence Diameter =

2

a

Diameter =

1.414

408

=288.5pm

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Answer 2

Answer:

The radius of the metal atom is $141.4pm$.

Therefore, option c) $141.4pm$ is the correct choice.

Explanation:

Data given,

The edge length of a unit cell, a = $400pm$

The lattice is a face-centered cubic lattice.

The radius of the metal atom, r =?

As we know,

• The radius for a face-centered cubic lattice is given by the formula:
• $4r = \sqrt{2}a$

Here,

• r = The radius of the metal atom
• a = The edge length of a unit cell

After putting the given values in the equation, we get:

• $4r = \sqrt{2}\times 400$
• r = $141.4 pm$

Hence, the radius of the metal atom, r = $141.4pm$