Magnesium has three naturally occurring isotopes: 24Mg, 25Mg, and 26Mg. If the atomic mass of magnesium is 24.305 u and the masses of the isotopes are 23.985 u (24Mg), 24.986 u (25Mg), and 25.983 u (26Mg), what is the fractional abundance of 24Mg if the abundances of 25Mg and 26Mg are 0.10 and 0.11, respectively?

• A. 0.21
• B. 0.79
• C. 0.89
• D. 0.10

Answer: (B)

Verified step by step guidance

1. Identify the given data: the atomic masses of the isotopes are 23.985 u for 24Mg, 24.986 u for 25Mg, and 25.983 u for 26Mg. The fractional abundances of 25Mg and 26Mg are given as 0.10 and 0.11, respectively.
2. Let the fractional abundance of 24Mg be represented as \(x\). Since the total fractional abundances must sum to 1, write the equation: \(x + 0.10 + 0.11 = 1\).
3. Solve for \(x\) to find the fractional abundance of 24Mg: \(x = 1 - (0.10 + 0.11)\).
4. Use the weighted average formula for atomic mass to check consistency: \(\text{Atomic mass} = (x)(23.985) + (0.10)(24.986) + (0.11)(25.983)\).
5. Substitute the value of \(x\) into the weighted average formula and verify that it equals the given atomic mass of 24.305 u to confirm the solution.