solution:
a) To calculate the volume of cube of edge 1.0cm
Volume= (edge)³
=(100cm) ³
= 1cm³
To find the mass of MG atoms
Density = mass/volume
Mass of mg = 1.74g/cm³ x 1cm³
= 1.74g
To find the number of mg atoms,
Molar mass of mg = 24.31g
24.31g mg contain 6.022 x 10²³ atoms of mg
1.74g mg contain = 6.022 x 10²³mg atoms/24.31g mg x 1.74g mg
= 0.4310 x 10²³mg atoms
= 4.31 x 10²² mg atoms
B) to find the volume occupied by mg atoms
Total volume of cube = 1 cm³
Volume occupied by mg atoms
= 74% of 1cm³
=74/100 x 1cm³= 0.74cm³
To find the volume of 1 mg atom
4.31 x 10²² mg atoms occupy 0.74 cm³
1 atom will occupy 0.74cm³
1 atom will occupy = 0.74cm³/4.31 x 10²²mg atoms x 1mg atom
volume of 1 mg atom = 0.1716 x 10⁻²²cm²
Volume of 1 mg atom = 4/3 π³ in the form of sphere.
4/3πr³ = 0.1716 x 10⁻²²cm³
R³ = 0.1716 x 10⁻²²cm³x 4/3 x 7/22
R³ = 0.04095 x 10⁻²²cm³
R = 0.1599 x 10⁻⁷cm
1 = 10⁻¹⁰cm
= 0.1599 x 10⁻⁷cm
= 1pm/1 x 10⁻¹⁰cm x 0.1599 x 10-7cm
= 1.599 x 10² pm
R= 1.6 x 10²pm
