Question

Calculate the number of atoms contained in a cylinder 1*10^-6 m in diameter by 1*10^-6 m deep of (a) magnesium (b) lead.

Answer 1

given :

Dimeter of the dylinder = 1E-6 m and depth = 1E-6m

Lets use volume formula of cylinder.

Volume of cylinder = pr²h

= 3.14 x ( 1E-6 / 2 m )² x 1E-6 m

=5.02E-18 m³

a). Number of magnesium atoms :

Atomic radius of Mg atom = 145 pm

Conversion of radius to m

Radius of Mg in m = 145 pm x 1 E-12 m / 1 pm

= 145E-12 m

= 1.45E-10 m

Number of Mg atoms = Total volume of cylinder / volume of each Mg atom

Since atom is in spherical shape, volume of Mg atom = 4 r³ = 4 x 3.14 x (1.45 E-10 m)

= 3.83E-29 m³

Number of Mg atoms = 5.02 E-18 m³/ 3.83 E-29 m³

= 1.31 E 11

b). Atomic radius of lead = 154 pm = 154 E-12 m = 1.54 E -10 m

Number of lead atoms = 5.02 E-18 m³ / 4 x 3.14 x (1.54 E-10 m)³

            = 1.10 E9 lead atoms