Question

The density of mercury is 13.6g/ml.calculate the diameter of an atom of mercury assuming that each atom of mercury is occupying a cube of edge -length equal to the diameter of the mercury atom. (Hg=200)

Answer 1

Here, we have to observe that we've been asked the volume of 1 atom of Hg in cm³

So, it would be convenient if we convert the density to atoms/cm³

Given, density (d) = 13.6g/mL

1 mole = 200g of Hg

i.e. 1g = 1/200 moles

d = 13.6 x 1/200 (moles/mL)

1 mole = 6.023 x 10²³ atoms

d = 13.6 x 1/200 x 6.023 x 10²³ (atoms/mL)

d = 4.095 x 10²² atoms/ml

As we're asked to find the diameter of one atom,

Vol. = 1 (atom)/4.095 x 10²² (atoms/mL)

Vol. = 2.44 x 10²³ mL

a³= 2.44 x 10²³ cc (Vol. of a cube = a³)

a = 2.9 x 10⁸ cm

d = 2.9 x 10⁸ cm (diameter of atom = edge length of cube)

Answer 2

Answer:

2.9×10^-8

Explanation:

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