This question involves the concepts of density, volume, and mass.
The approximate diameter of a magnesium atom is "3.55 x 10⁻¹⁰ m".
It is given that:
Mass of one mole = 24 grams
Mass of 6 x 10²³ atoms = 24 grams
Mass of 1 atom = [tex]\frac{24\ grams}{6\ x\ 10^{23}\ atoms}[/tex] = 4 x 10⁻²³ grams
[tex]\rho = \frac{m}{V}\\\\V=\frac{m}{\rho}[/tex]
where,
Therefore,
[tex]V=\frac{4\ x\ 10^{-23}\ grams}{1.7\ grams/cm^3}[/tex]
V = 2.35 x 10⁻²³ cm³
The atom is in a spherical shape. Hence, its Volume can be given as follows:
[tex]V =\frac{\pi d^3}{6}\\\\d=\sqrt[3]{ \frac{6V}{\pi}}\\\\d=\sqrt[3]{ \frac{6(2.35\ x\ 10^{-23}\ cm^3)}{\pi}}[/tex]
d = 0.355 x 10⁻⁷ cm = 3.55 x 10⁻¹⁰ m
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