Gallium crystallizes in a primitive cubic unit cell. The length of the unit cell edge is 3.70 Å. The radius of a Ga atom is ________ Å.
A)7.40
B)3.70
C)1.85
D)0.930
E)Insufficient data is given.

Question

Quizplus · Accepted Answer

In a primitive cubic unit cell, the atoms are located at the corners of the cube, and each atom touches the atoms in the adjacent corners. Therefore, the length of the diagonal of the unit cell is equal to four times the radius of a Ga atom. Using the Pythagorean theorem, we can calculate the diagonal length:

diagonal^2 = edge^2 + edge^2 + edge^2 = 3(edge)^2 
diagonal^2 = 3(3.70 Å)^2 
diagonal = 2.55 Å

Thus, the radius of a Ga atom is:

radius = diagonal/4 = 2.55 Å/4 = 0.6375 Å ≈ 0.930 Å

Gallium Crystallizes in a Primitive Cubic Unit Cell