How many atoms are in a sample of 68.7 g of copper

First, you must find the number of moles of copper that your sample has. This is calculated by #of moles= your sample mass (in grams)/ atomic mass (in grams) 
#of moles=68.7g/63.546g
#of moles= 1.08 moles present 

Then to find the number of atoms present, we must multiply the number of moles present in the sample with Avogadro's number, which is 6.022x10^23 (this number is the number of atoms present in each mole)
# of atoms present in copper sample=1.08(6.022x10^23)
#of atoms present in copper sample= 6.50x10^23

Outermost (valence) electrons