Germanium has five naturally occurring isotopes: 70^Ge, 20.5%, 69.924; 72^Ge, 27.4%, 71.922; 73^Ge, 7.8%, 72.923; 74^Ge, 36.5%, 73.921; and 76^Ge, 7.8%, 75.921. What is the atomic weight of germanium?

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Identify the mass number and relative abundance for each isotope of Germanium. For example, for the isotope 70^Ge, the mass number is 69.924 and its abundance is 20.5%.

Convert the percentage abundance of each isotope into a decimal by dividing by 100. For instance, 20.5% becomes 0.205.

Multiply the mass number of each isotope by its decimal abundance to find the weighted contribution of each isotope to the overall atomic weight. For 70^Ge, this would be 69.924 multiplied by 0.205.

Sum the weighted contributions of all isotopes to get the total atomic weight of Germanium. Add the results from the previous step for all isotopes.

The sum calculated in the previous step represents the atomic weight of Germanium.

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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, germanium has several isotopes, each with a unique mass and natural abundance, which contribute to the element's average atomic weight.

Atomic Weight Calculation

The atomic weight of an element is calculated as the weighted average of the masses of its isotopes, taking into account their relative abundances. This involves multiplying the mass of each isotope by its percentage abundance (expressed as a fraction) and summing these values to obtain the overall atomic weight.

Percentage Abundance

Percentage abundance refers to the proportion of each isotope of an element present in a natural sample, expressed as a percentage. In the case of germanium, each isotope's abundance must be converted to a decimal fraction to accurately calculate the weighted average for the atomic weight.