In this question, we have to find the mass of 5.42*10^21 atoms of platinum.
In order to find this value, the first thing we need to do is to find out how many moles of Platinum we have, we will be using this number of atoms, and the Avogadro's number, which is the number of atoms of any element in 1 mol.
Avogadro's number = 6.02*10^23 atoms in 1 mol of the element
Using this value, we can find the number of moles of Platinum:
6.02*10^23 atoms = 1 mol
5.42*10^21 atoms = x moles
6.02*10^23x = 5.42*10^21
x = 5.42*10^21/6.021*10^23
x = 0.009 moles of Platinum in 5.42*10^21 atoms
Now that we have the number of moles of Platinum, 0.009 moles, we will find the mass of this number of moles. In order to do that, we will be using the molar mass of Platinum, which is the total mass of this element present in 1 mol
Molar mass of Platinum = 195g/mol, there is 195 grams in 1 mol of Pt
1 mol = 195 grams
0.009 moles = x grams
x = 195 * 0.009
x = 1.75 grams of Platinum
The answer will be: There is 1.75 grams of Platinum in 5.42*10^21 atoms of this element