Which of the following numerical setups can be used to calculate the atomic mass of silver, given that silver has two naturally occurring isotopes: Ag-107 (abundance: 51.8%, mass: 106.905 amu) and Ag-109 (abundance: 48.2%, mass: 108.905 amu)?

• A. (0.482 × 106.905) + (0.518 × 108.905)
• B. (106.905 + 108.905) / 2
• C. (0.518 × 106.905) + (0.482 × 108.905)
• D. (51.8 × 106.905) + (48.2 × 108.905)

Answer: (C)

Verified step by step guidance

1. Understand that the atomic mass of an element with multiple isotopes is calculated as the weighted average of the masses of its isotopes, where the weights are their relative abundances expressed as decimals.
2. Convert the given percentage abundances of the isotopes into decimal form by dividing by 100. For example, 51.8% becomes 0.518 and 48.2% becomes 0.482.
3. Set up the weighted average formula for atomic mass: \(\text{Atomic Mass} = (\text{fractional abundance of isotope 1} \times \text{mass of isotope 1}) + (\text{fractional abundance of isotope 2} \times \text{mass of isotope 2})\).
4. Substitute the correct fractional abundances and isotope masses into the formula, ensuring that the abundance for Ag-107 (51.8% or 0.518) is multiplied by its mass (106.905 amu), and the abundance for Ag-109 (48.2% or 0.482) is multiplied by its mass (108.905 amu).
5. Avoid common mistakes such as mixing up the abundances with the wrong isotope masses, using percentages directly without converting to decimals, or simply averaging the masses without weighting by abundance.