Problem: Barium has a density of 3.59 g/cm3  and crystallizes with a body-centered cubic unit cell. Calculate the radius of a barium atom.

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FREE Expert Solution

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 the edge length (a) of a BCC unit cell can be calculated using the equation:


a=4r3


Step 1: Calculate the volume of 1 unit cell using density

  • molar mass Ba = 137.33 g/mol
  • 1 mole = 6.022x1023 entities (Avogadro' number)
    entities = atoms, ions, molecules, formula units


recall the # of atoms present per 1 BCC unit cell: corner atoms contribute 1/8 and the center atom contribute 1

# of atoms=8×18+1

# of atoms = 2 per 1 unit cell


Solving volume of 1 unit cell:


volume=137.33 g Ba1 mol Ba×1 mol Ba(6.022×1023) Ba atoms×2 Ba atoms1 unit cell ×1 cm33.59 g Ba

volume =1.27x10-22 cm3/1 unit cell


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Problem Details

Barium has a density of 3.59 g/cm3  and crystallizes with a body-centered cubic unit cell. Calculate the radius of a barium atom.

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Unit Cell concept. You can view video lessons to learn Unit Cell. Or if you need more Unit Cell practice, you can also practice Unit Cell practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor N/A's class at Ryerson University.