Antimony has two naturally occurring isotopes: Sb-121 with a mass of 120.904 amu and a natural abundance of 57.21%, and Sb-123. If the atomic mass of antimony is 121.760 amu, what is the mass of Sb-123?

• A. 121.760 amu
• B. 123.760 amu
• C. 122.904 amu
• D. 120.904 amu

Answer: (C)

Verified step by step guidance

1. Understand that the atomic mass of an element is the weighted average of the masses of its isotopes, based on their natural abundances.
2. Set up the equation for the average atomic mass: \( \text{Atomic Mass} = (\text{Mass of Sb-121} \times \text{Abundance of Sb-121}) + (\text{Mass of Sb-123} \times \text{Abundance of Sb-123}) \).
3. Substitute the known values into the equation: \( 121.760 = (120.904 \times 0.5721) + (\text{Mass of Sb-123} \times (1 - 0.5721)) \).
4. Solve for the mass of Sb-123 by isolating it on one side of the equation. First, calculate the contribution of Sb-121 to the atomic mass, then rearrange the equation to solve for the mass of Sb-123.
5. Calculate the mass of Sb-123 using the rearranged equation and the known values. This will give you the mass of Sb-123 in amu.