2017 H2 Chem P1 Q1 — Atomic structure Solution

The answer is C (5.54%).
The relative atomic mass is the abundance-weighted average of the isotopic masses. Let the percentage of \(^{29}\text{Si}\) be \(x\). Then the percentage of \(^{30}\text{Si}\) is \(100 - 92.23 - x = 7.77 - x\).
\(\dfrac{92.23 \times 28 + 29x + 30(7.77 - x)}{100} = 28.10\)
\(2582.44 + 29x + 233.1 - 30x = 2810\)
\(2815.54 - x = 2810\), so \(x = 5.54\)
The sample contains 5.54% \(^{29}\text{Si}\) (and \(7.77 - 5.54 = 2.23\)% \(^{30}\text{Si}\)).
• A is wrong: 2.23% is the percentage of \(^{30}\text{Si}\), not \(^{29}\text{Si}\).
• B is wrong: 3.89% is half of 7.77%, which assumes the two heavier isotopes are equally abundant. That gives \(A_\text{r} = 0.9223(28) + 0.0389(29) + 0.0389(30) = 28.12\), not 28.10.
• D is wrong: 7.77% is the combined percentage of \(^{29}\text{Si}\) and \(^{30}\text{Si}\), not \(^{29}\text{Si}\) alone.