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How can you determine the number of atoms per nm3 in potassium?

Based on the given data, what is the process involved in calculating the number of potassium atoms per nm3?

Answer:

To calculate the number of potassium atoms per nm3, the density of potassium is divided by its molar mass to determine the number of moles, which is then multiplied by Avogadro's number. The result is then converted from atoms per cm3 to atoms per nm3. Number of atoms per nm3 = 137 atoms/nm3

Explanation:

To calculate the number of potassium atoms per nm3, we first need to find the number of moles in 1 cm3 of potassium. The density of potassium is given as 0.89 g/cm3, and its molar mass is 39.098 g/mol.

To find the moles of potassium in 1 cm3, we use the formula:

Number of moles = Mass (g) / Molar mass (g/mol)

Number of moles = 0.89 g/cm3 / 39.098 g/mol = 0.0228 mol/cm3

Now, to find the number of atoms, we multiply the moles by Avogadro's number (6.02 × 10^23 atoms/mol):

Number of atoms = (0.0228 mol/cm3) × (6.02 × 10^23 atoms/mol)

Number of atoms = 1.37 × 10^22 atoms/cm3

To convert cm3 to nm3, remember that 1 cm3 is equal to 10^21 nm3. Hence, divide the number of atoms by 10^21 to find atoms per nm3:

Number of atoms per nm3 = (1.37 × 10^22 atoms/cm3) / (10^21 nm3/cm3)

Number of atoms per nm3 = 137 atoms/nm3