An element Z contains 80% of $^{16} _8$Z and 20% of $^{18} _8$Z. Its relative atomic mass is

Analysis

The question asks for the relative atomic mass of an element that exists as a mixture of two isotopes. To find this, we calculate the weighted average of the mass numbers based on their percentage abundance in nature.

Concept

The relative atomic mass of an element is calculated using the formula:

Where:

• Isotope Mass is the mass number of each isotope.
• Fractional Abundance is the percentage divided by 100.

Step-by-Step Solution

1. Identify the data provided: • Isotope 1: Mass = 16, Abundance = 80% (or 0.80) • Isotope 2: Mass = 18, Abundance = 20% (or 0.20)

2. Calculate the contribution of each isotope: • Contribution of Isotope 1: $16 \times 0.80 = 12.8$ • Contribution of Isotope 2: $18 \times 0.20 = 3.6$

3. Sum the contributions to find the relative atomic mass: • Relative Atomic Mass $= 12.8 + 3.6$ • Relative Atomic Mass $= 16.4$

Conclusion

Comparing our result to the options provided, the calculated value is 16.4.

Exam Tip: When calculating relative atomic mass from isotopes, your final answer should always fall between the mass numbers of the two isotopes. Since 16.4 is between 16 and 18, it is a logical result. If you get a number outside that range, you know you've made a calculation error!