Polonium crystallizes with a primitive cubic structure. It has a density of 9.4 g/cm³, a radius of 167 pm, and a molar mass of 209 g/mol. Calculate the number of atoms in one mole of Polonium.

• A. 6.0×10^-23
• B. 3.2×10¹¹
• C. 6.0×10²³
• D. 1.7×10¹⁵

Answer: (C)

Verified step by step guidance

1. Understand that the problem is asking for the number of atoms in one mole of Polonium, which is essentially Avogadro's number. This is a fundamental constant in chemistry, approximately 6.022 x 10^23 atoms/mol.
2. Recognize that the given density, radius, and molar mass are not directly needed to find Avogadro's number, as it is a known constant. However, these values are typically used to calculate the number of atoms in a unit cell or to verify the structure type.
3. Recall that a primitive cubic structure has one atom per unit cell. This information is useful if you were calculating the number of atoms in a given volume or verifying the density.
4. If you were to use the density, radius, and molar mass to find the number of atoms in a unit cell, you would use the formula: \( \text{Density} = \frac{\text{Molar Mass}}{\text{Volume of Unit Cell} \times \text{Avogadro's Number}} \). However, this is not necessary for this problem.
5. Conclude that the number of atoms in one mole of any element, including Polonium, is Avogadro's number, which is approximately 6.022 x 10^23 atoms/mol. This is a constant value and does not change with the element.