An unknown metal crystallizes in a primitive cubic unit cell.The length of the unit cell edge is 2.85 Å.The radius of the unknown atom is ________ Å.
A)5.70
B)1.43
C)1.85
D)1.01
E)Insufficient data is given.

Question

Quizplus · Accepted Answer

In a primitive cubic unit cell, only one atom is present at the corners of the cube. The diagonal distance between opposite corners of a cube can be calculated using the Pythagorean theorem:

(diagonal)² = (a)² + (a)² + (a)²
(diagonal)² = 3a²
diagonal = √3a

In this case, the diagonal distance is equal to four times the atomic radius because it passes through the center of the cube. Therefore:

4r = √3a
r = √3a/4

Plugging in the given values:

r = √3(2.85Å)/4 = 1.43 Å

Therefore, the answer is B.

An Unknown Metal Crystallizes in a Primitive Cubic Unit Cell