Calculate the radius of tantalum (ta) atom, given that ta has a bcc crystal structure, a density of 16.6 g/cm, and an atomic weight of 180.9 g/mol. (avogadro number, 6.023 x 103 atoms/mol).

The radius of tantalum (Ta) atom is

Explanation:

From the Body-centered cubic (BBC) crystal structure we know that a unit cell length a and atomic radius R are related through

So the volume of the unit cell is

We can compute the theoretical density ρ through the following relationship

where

n = number of atoms associated with each unit cell

A = atomic weight

= volume of the unit cell

=  Avogadro’s number ( atoms/mol)

From the information given:

A = 180.9 g/mol

ρ = 16.6 g/cm^3

Since the crystal structure is BCC, n, the number of atoms per unit cell, is 2.

We can use the theoretical density ρ to find the radio R as follows:

Solving for R

Substitution for the various parameters into above equation yields

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