Thank you for the opportunity to help you with your question!
First you have to find the volume of a sphere with a 5.0mm diameter. To get the radius you divide the diameter by two 5.0/ 2 = 2.5 mm Then you need to convert this into cm. There are 10 mm in one cm. 2.5 mm / 10 mm *1 cm for conversion = .25 cm. This equals r.
Volume is 4/3 pi .25^3 or .06541667 cm^3
Since the density of silver is 10.49 g / cm^3 you can use this value and multiply what the volume is to get the amount of g of silver. 10.49 * .06541667 = .68622083 g of silver
Then you convert the g of silver into moles using the molar mass of silver which is 107.868 g/ mol so you have the equation of .68622083 g / 107.868 g * mol = .00636167 mol of silver.
In one mol there are 6.023 X 10^23 atoms in it. Then you take .00636167 * 6.023x10^23 which equals
3.8 x 10^21 atoms
Please let me know if you need any clarification. I'm always happy to answer your questions.