The element lead (Pb) consists of four naturally occurring isotopes with atomic masses 203.97302, 205.97444, 206.97587, and 207.97663 amu. The relative abundances of these four isotopes are 1.4, 24.1, 22.1, and 52.4%, respectively. From these data, calculate the atomic weight of lead.

Verified step by step guidance

1. Convert the percentage abundances of each isotope into decimal form by dividing each by 100.
2. Multiply the atomic mass of each isotope by its corresponding decimal abundance to find the weighted mass contribution of each isotope.
3. Add all the weighted mass contributions together to find the total atomic weight of lead.
4. Ensure that the units are consistent and the final atomic weight is expressed in atomic mass units (amu).
5. Review the calculation to ensure that all steps have been followed correctly and that the sum of the abundances equals 100%.

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 lead (Pb), there are four isotopes with distinct atomic masses, which contribute to the element's average atomic weight based on their relative abundances.

Relative Abundance

Relative abundance refers to the proportion of each isotope of an element present in a sample, usually expressed as a percentage. In the case of lead, the relative abundances of its isotopes are crucial for calculating the weighted average atomic mass, as each isotope's contribution to the overall atomic weight is proportional to its abundance.

Weighted Average

The weighted average is a calculation that takes into account the different weights (or contributions) of each component in a dataset. To find the atomic weight of lead, the atomic masses of its isotopes are multiplied by their respective relative abundances, and the results are summed and divided by 100 to yield the average atomic weight.