Open Question
How many total (or composite) atoms are contained in a unit cell of primitive cubic arrangement?
13. Liquids, Solids & Intermolecular Forces
Simple Cubic Unit Cell
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Gallium crystallizes in a primitive cubic unit cell. The length of an edge of this cube is 362 pm. What is the radius of a gallium atom?
A
724 pm
B
90.5 pm
C
181 pm
D
362 pm
Verified step by step guidance1
Understand that in a primitive cubic unit cell, each corner of the cube is occupied by an atom, and the atoms touch each other along the edge of the cube.
In a primitive cubic unit cell, the edge length of the cube is equal to twice the radius of the atom. This is because the atoms at the corners touch each other along the edge.
Given that the edge length of the cube is 362 pm, set up the equation for the edge length in terms of the radius: \( 2r = 362 \text{ pm} \), where \( r \) is the radius of a gallium atom.
Solve the equation \( 2r = 362 \text{ pm} \) for \( r \) by dividing both sides by 2.
The result from the calculation will give you the radius of a gallium atom in picometers (pm).
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