The atomic radius of lithium can be determined using its crystal structure and the dimensions of its unit cell. Lithium has a body-centered cubic (BCC) structure.
Understanding the BCC Structure
In a BCC structure, atoms are located at the corners of the cube and one atom is in the center of the cube. This arrangement affects how we calculate the atomic radius.
Key Relationships
- Edge Length (a): The length of one side of the cubic unit cell.
- Atomic Radius (r): The radius of a single lithium atom.
- Relationship in BCC: In a BCC structure, the atoms touch along the body diagonal. The body diagonal is equal to four times the atomic radius (4r), and it's also related to the edge length (a) by the equation: √3a.
Calculation Steps
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Determine the edge length (a): This value would need to be determined experimentally, often through X-ray diffraction.
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Apply the formula: Since the body diagonal is equal to 4r, and is also equal to √3a, the following relationship holds: 4r = √3a. Solving for the atomic radius:
- r = (√3/4)a
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Use given reference: The provided reference states: ⇒r=√34×351=151.9 pm. This already incorporates the above steps and provides a calculation result and the atomic radius of lithium, specifically, 151.9 pm. This implies the edge length (a) is 351 pm for a given measurement, and the radius has been calculated from it.
Example
Let's use the value from the reference. Here's how we determine the result:
- Given edge length a= 351 pm (from the reference)
- r = (√3/4)a
- r = (√3/4) * 351 pm
- r = 151.9 pm
Summary
| Aspect | Description |
|---|---|
| Crystal Structure | Body-Centered Cubic (BCC) |
| Atoms Touch | Along the body diagonal of the unit cell |
| Formula | r = (√3/4)a, where 'a' is the edge length of the cubic unit cell |
| Calculated Radius (from reference) | 151.9 pm |
Therefore, to find the atomic radius of lithium, determine the edge length of its unit cell via experimental methods and apply the formula, or utilize reference material that contains the result, such as the one given above, which gives the radius as 151.9 pm.
