A pure copper sphere has a radius of 0.935 in. How many copper atoms does it contain? [The volume of a sphere is (4>3)pr3 and the density of copper is 8.96 g>cm3.]

47.68 x 10²³ or 4.768 x 10²⁴ copper atoms

Explanation:

Given:

Radius of the copper sphere (r) = 0.935 in

First convert the radius from inches to centimeters

1 in = 2.54cm

0.935in =  0.935 x 2.54cm = 2.3749cm

∴ r = 2.3749cm

Calculate the volume of the copper sphere as follows

Volume =          [substitute r = 2.3749cm and π = 22 / 7]

Volume =

Volume = 56.108cm³

From the volume and given density, calculate the mass of the copper sphere

mass = density x volume           [density = 8.96g/cm³]

mass = 8.96 x 56.108 = 502.73g

From known facts

1 mole of copper = 63.5g of copper = 6.022 x 10²³ copper atoms.

Then,

502.73 g of copper =  = 47.68 x 10²³ copper atoms

Therefore, the sphere contains 47.68 x 10²³ copper atoms

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