An unknown metal crystallizes in a body-centered cubic structure with a unit cell edge length of 4.35 Å.The radius of the unknown atom is ________ Å.
A)1.88
B)3.77
C)2.18
D)8.70
E)4.35

Question

Quizplus · Accepted Answer

In a body-centered cubic (bcc) structure, the diagonal across the body of the cube, which passes through the center, is equal to 4 times the radius of the atom (4r). This diagonal can also be calculated using the Pythagorean theorem in three dimensions as √3 times the edge length (a), so 4r = a√3. Given the edge length (a) is 4.35 Å, the radius (r) of the atom can be calculated as (4.35 Å * √3) / 4, which equals approximately 1.88 Å.

An Unknown Metal Crystallizes in a Body-Centered Cubic Structure with a Unit