A metal crystallizes with a cubic structure having edge length of 200 pm. if there are two metal atoms per unit cell, then the diameter of one metal atom is?
Answers
Since there are two atoms per unit cell and metal crystallizes in cubic structure, we can conclude that the crystal structure of the metal is body centered cubic structure.
(please refer the attachment for figure)
From the figure, In ΔEFD ( ΔEFD lies on bottom plane)
b² = a² + a²
b = √2a
Now in ΔAFD ( ΔAFD lies on the base FD)
c² = a² + b² = a² + 2a² = 3a²
The length of the diagonal from corner E to B is 4r, where r is the radius of atom (which we are intended to find).
Therefore, √3a = 4r
⇒ r = (√3/4)a
Now from the question, a = 200 pm
Hence, radius of atom ⇒ r = (√3/4) x 200 pm
= 50√3 pm
= 86.6 pm
Answer:
Explanation:
Since there are two metal atoms in the lattice its of cscl type and for cscl type lattice (3)^1/2a=2r so the ans is 173
Hpe it helps