Final answer:
To calculate the number of atoms per nm3 in potassium, one must convert the given density to the correct units, find the number of moles based on density and atomic weight, and then use Avogadro's number to determine the number of atoms.
Step-by-step explanation:
The question asks us to calculate the number of atoms per nm3 in potassium (K), given its density and atomic weight. To find the number of atoms, we will first need to determine the number of moles of potassium in 1 nm3 and then use Avogadro's number to find the number of atoms.
Firstly, the density of potassium is given as 0.89 g/cm3, which needs to be converted into g/nm3. Since there are 1e21 nm3 in 1 cm3, this becomes 0.89 x 1e21 g/nm3.
Next, we use the atomic weight of potassium, 39.098 g/mol, to determine moles in 1 nm3. We know that the number of moles is the mass divided by the molar mass, so:
number of moles = 0.89 x 1e21 g/nm3 / 39.098 g/mol
Finally, to find the number of atoms, we multiply the number of moles by Avogadro's number (approximately 6.022 x 1023 atoms/mol):
number of atoms per nm3 = (0.89 x 1e21 / 39.098) x 6.022 x 1023