Silver has an atomic mass of 107.868 amu. The Ag-109 isotope (108.905 amu) is 48.16%. What is the amu of the other isotope?

• A. 106.905 amu
• B. 106.908 amu
• C. 106.903 amu
• D. 106.911 amu

Answer: (A)

Verified step by step guidance

1. Understand that the atomic mass of silver is a weighted average of its isotopes. This means the atomic mass is calculated based on the relative abundance of each isotope.
2. Let the atomic mass of the unknown isotope be represented as \( x \). The equation for the average atomic mass is: \( 107.868 = (x \times \text{abundance of unknown isotope}) + (108.905 \times 0.4816) \).
3. Since the abundance of the Ag-109 isotope is 48.16%, the abundance of the unknown isotope is \( 100\% - 48.16\% = 51.84\% \) or \( 0.5184 \) in decimal form.
4. Substitute the abundance values into the equation: \( 107.868 = (x \times 0.5184) + (108.905 \times 0.4816) \).
5. Rearrange the equation to solve for \( x \): \( x = \frac{107.868 - (108.905 \times 0.4816)}{0.5184} \).