The atomic radius of a metal is determined by measuring the distance between the nuclei of two adjacent metal atoms that are chemically bonded and then dividing that distance by two.
Understanding Atomic Radius Measurement
Atomic radius is essentially half the distance between the nuclei of two identical atoms that are bonded together. When it comes to metals, the method relies on understanding how metal atoms arrange themselves in a crystal lattice structure. Metals don't form conventional molecules, so this approach is fundamental to their radius measurement.
Steps to Determine Atomic Radius of a Metal:
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Crystal Structure Analysis: Metals often form repeating structures called crystal lattices. The first step involves analyzing the crystal structure using techniques like X-ray diffraction. This helps determine the distance between the nuclei of neighboring metal atoms.
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Measuring Interatomic Distance: This distance is the shortest distance between the nuclei of adjacent atoms in the crystal structure.
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Calculating Atomic Radius: The atomic radius is then calculated by dividing this measured interatomic distance by two. According to the reference, "the atomic radius is calculated by measuring the distance between the nuclei of two identical atoms bonded together. Half this distance is the atomic radius."
Practical Insights:
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Bonding Type: The method works because metal atoms are held together by metallic bonds. These are non-directional bonds that allow atoms to pack closely together, making the measurement of interatomic distance reliable.
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Types of Atomic Radius: While this method helps determine the atomic radius in the metallic bonding scenario, keep in mind that atomic radius can also be defined and measured differently, depending on the chemical environment such as covalently bound atoms or van der Waals interactions. However, for metals, the method explained above is common.
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X-ray Diffraction: The method of measuring the distance is often done using x-ray diffraction which allows scientist to see distances on atomic scales.
Example
Suppose that in a sample of copper metal, the distance between the nuclei of two copper atoms is measured to be 256 picometers (pm). The atomic radius of a copper atom would be half of this distance:
256 pm / 2 = 128 pm
Therefore, the atomic radius of copper in this metallic state would be approximately 128 pm.
