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The density of mercury is 13.6 g/mL. The...

The density of mercury is 13.6 g/mL. The diameter of an atom of mercury assuming that each atom is occupying a cube of edge length equal to the diameter of the mercury atom is approximately

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The correct Answer is:
`2.90 xx 10^(-8)cm`
Suppose the diameter of an atom of Hg is x cm. Since, the Hg atom is assumed to occupy the edge length equal to its diameter the volume occupied by one atom of Hg will be `x^3`.
Mass of one atom of `Hg=(200)/(6.023 xx 10^(23)) g`
(Atomic mass of Hg=200)
`"Density "=("Mass")/("Volume")`
`13.6=(200)/((6.023 xx 10^(23))/(x^3))`
`or x^3=(200)/(6.023 xx 10^(23)) xx 1/(13.6)`
`or x=2.90 xx 10^(-8)cm`
Hence, the diameter of an atom of mercury is `2.90 xx 10^(-8)cm`.
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