Magnesium has three naturally occurring isotopes: ²⁴Mg (23.985) with 78.99% abundance, ²⁵Mg (24.986) with 10.00% abundance, and a third with 11.01% abundance. Look up the atomic weight of magnesium, and then calculate the mass of the third isotope.

Verified step by step guidance

1. Identify the given isotopes and their respective abundances: \(^{24}\text{Mg}\) with 78.99% abundance, \(^{25}\text{Mg}\) with 10.00% abundance, and a third isotope with 11.01% abundance.
2. Use the formula for the average atomic mass: \( \text{Average Atomic Mass} = (\text{mass of } ^{24}\text{Mg} \times \text{abundance of } ^{24}\text{Mg}) + (\text{mass of } ^{25}\text{Mg} \times \text{abundance of } ^{25}\text{Mg}) + (\text{mass of third isotope} \times \text{abundance of third isotope}) \).
3. Look up the average atomic mass of magnesium from the periodic table, which is approximately 24.305 u.
4. Set up the equation using the known values: \( 24.305 = (23.985 \times 0.7899) + (24.986 \times 0.1000) + (\text{mass of third isotope} \times 0.1101) \).
5. Solve the equation for the mass of the third isotope by isolating it on one side of the equation.

Key Concepts

Isotopes

Isotopes are variants of a chemical element that have the same number of protons but different numbers of neutrons, resulting in different atomic masses. For example, magnesium has three isotopes: 24Mg, 25Mg, and a third isotope. Understanding isotopes is crucial for calculating average atomic weights and determining the mass of individual isotopes based on their relative abundances.

Atomic Weight

The atomic weight of an element is the weighted average of the masses of its isotopes, taking into account their relative abundances. It is typically expressed in atomic mass units (amu). To find the atomic weight of magnesium, one must consider the contributions of each isotope based on their abundance, which is essential for solving the problem of finding the mass of the third isotope.

Weighted Average Calculation

Calculating a weighted average involves multiplying each value by its corresponding weight (or abundance) and then summing these products before dividing by the total weight. In this context, to find the mass of the third magnesium isotope, one would set up an equation using the known atomic weight and the abundances of the other isotopes, allowing for the determination of the unknown mass.