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Problem: Iron (Fe) has a BCC crystal structure, an atomic radius of 0.124 nm, and an atomic weight of 55.85 g/mol. What is its theoretical density in g/cm3?

FREE Expert Solution

We’re being asked to calculate the density of Fe that crystallizes in a body-centered cubic unit cell.


A body-centered cubic (BCC) unit cell is composed of a cube with one atom at each of its corners and one atom at the center of the cube


Recall that density has a formula of:

density=massvolume

mass = g
volume = cm3


We’re going to calculate for the density of Fe using the following steps:

Step 1:Calculate the edge length from the atomic radius
Step 2: Calculate the volume of the 1 unit cell
Step 3: Calculate the density of the Fe



Step 1: Calculate the edge length from the atomic radius

a=4r3a=4(0.124 nm)3×10-7 cm1 nm

a= 2.86x10-8 cm


Calculate the volume of the unit cell.

In a BCC unit cell:


Given: edge length (a) = 5.025 Å

volume of unit cell=volume of cubevolume of unit cell=a3volume of unit cell =( 2.86×10-8 cm)3

volume of unit cell = 2.35 x 10-23 cm3


Step 3: Calculate the density of the Fe


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Problem Details

Iron (Fe) has a BCC crystal structure, an atomic radius of 0.124 nm, and an atomic weight of 55.85 g/mol. What is its theoretical density in g/cm3?

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