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The density of mercury is 13.6 g mL^(-1)...

The density of mercury is `13.6 g mL^(-1)`. Calculate the approximate 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.

A

3.01 Å

B

2.54 Å

C

0.29 Å

D

2.91 Å

Text Solution

Verified by Experts

The correct Answer is:
D
`N_A=6.023xx10^23`
Atomic mass of mercury =200
Number of atoms present in 200 g of Hg = `6.023xx10^23`
So, number of atoms present in 1 g of Hg =`(6.023xx10^23)/200`
`=3.0115xx10^21`
Density of Hg=13.6 g/cc
Volume of 1 atom of mercury (Hg) `=1/(3.0115xx10^21xx13.6)`cc=`2.44xx10^(-23)`cc
As each mercury atom occupies a cube of edge length equal to its diameter, therefore Diameter of 1 mercury atom = `(2.44xx10^(-23))^(1//3)` cm
`=2.905xx10^(-8)` cm =2.91 Å
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