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Here's a guess... Without getting overly complicated.... The diameter of the atom isn't just the diameter of the atom's nucleus... it is the diameter of the whole atom including the electron cloud surrounding the nucleus. As the name implies, an electron cloud represents all the possible locations that the electron could be. This cloud has thickness and therefore the atom could be smaller if the electron is in a portion of the cloud closer to the nucleus or larger is the electron is in a portion of the cloud farther from the nucleus. The "known value" is probably just the average of the two. Therefore, an atom's diameter has a range rather than a fixed value.

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Q: Can you explain why the estimation of the diameter of an atom is greater or less than the known value?
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