The volume of a sphere is (4/3) πr3 and the density of copper is 8.96g/cm3.

What is the radius (in cm) of a pure copper sphere that contains 1.41*1024 copper atoms?

First, we need to get the mass of the copper, then we will use this mass along with the given density to find the volume and finally we will substitute in the rule of volume to get the radius.

First, calculating the mass:

number of atoms in one mole of an element = 6.022 x 10^23

So, we can use cross multiplication to find the number of moles containing 1.41*10^24 atoms as follows:

number of moles = (1.41*10^24 x 1) / (6.022 x 10^23) = 2.3414 moles

From the periodic table:

molar mass of copper = 63.5 grams

number of moles = mass / molar mass

2.3414 = mass / 63.5

mass = 2.3414 x 63.5 = 148.6789 grams

Then, we get the volume:

density = mass / volume

8.96 = 148.6789 / volume

volume = 16.59 cm^3

Finally, we get the radius:

volume = (4/3) x pi x (radius) ^3

16.59 = (4/3) x (22/7) x (radius) ^3

radius^3 = 3.9614

radius = 1.5822 cm