Atoms Per Nanometer Cubed in Potassium Calculation

How do we calculate the number of atoms per nm³ in potassium?

Using the density of potassium and its atomic weight, how can we determine the number of atoms in a nanometer cubed?

Answer:

To calculate the number of atoms of potassium per nm³, we need to utilize the density and atomic weight of potassium to find moles per nm³. Then, Avogadro's number will help us determine the count of atoms, resulting in approximately 1.371 × 10·¹ atoms/nm³.

Explanation:

To calculate the number of atoms per nanometer cubed (nm³) in potassium (K), we consider the density of potassium, its atomic weight, and Avogadro's number. The density of K is 0.89 g/cm³ and its atomic weight is 39.098 g/mol. First, we convert the density to grams per nanometer cubed (g/nm³):

1 g/cm³ = 1×10¹¹ g/nm³

So, 0.89 g/cm³ = 0.89 × 10¹¹ g/nm³.

To find moles per nanometer cubed, we divide the density by the atomic weight:

0.89 × 10¹¹ g/nm³ ÷ 39.098 g/mol = 2.277 × 10¹¹ mol/nm³

Using Avogadro's number, 6.022 × 10²³ atoms/mol, we can calculate the number of atoms per nanometer cubed:

2.277 × 10¹¹ mol/nm³ × 6.022 × 10²³ atoms/mol = 1.371 × 10·¹ atoms/nm³