$\beta$-tungsten crystallises with a body centred cubic structure where the length of the unit cell is 3.150 Å. Use the diagram to calculate the radius of a tungsten atom. (Hint: The radius of the atom is just half the distance between the two closest atoms.)

Question

Quizplus · Accepted Answer

In a body centered cubic structure, the atoms are arranged in a way that each atom has eight neighboring atoms. The distance between the two closest atoms is equal to the body diagonal of the cube, which can be calculated using the length of the unit cell (a) as follows:

body diagonal = a*sqrt(3)

= 3.15 Å * sqrt(3)

= 5.454 Å

The radius of a tungsten atom is half of the body diagonal, which is :

radius = 5.454 Å / 2

= 2.727 Å

Therefore, the radius of a tungsten atom is 1.346 Å (option C).

β\betaβ -Tungsten Crystallises with a Body Centred Cubic Structure Where the the Length

$\beta$ -Tungsten Crystallises with a Body Centred Cubic Structure Where the the Length