The nucleus of ⁶Li is a powerful absorber of neutrons. It exists in the naturally occurring metal to the extent of 7.5%. In the era of nuclear deterrence, large quantities of lithium were processed to remove ⁶Li for use in hydrogen bomb production. The lithium metal remaining after removal of 6Li was sold on the market. (b) The atomic masses of ⁶Li and ⁷Li are 6.015122 and 7.016004 u, respectively. A sample of lithium depleted in the lighter isotope was found on analysis to contain 1.442% ⁶Li. What is the average atomic weight of this sample of the metal?

Verified step by step guidance

1. Identify the atomic masses of the isotopes involved: 6Li has an atomic mass of 6.015122 u and 7Li has an atomic mass of 7.016004 u.
2. Determine the percentage of each isotope in the sample: 6Li is 1.442% and 7Li is the remainder, which is 100% - 1.442% = 98.558%.
3. Convert the percentages into decimal form for calculation: 1.442% becomes 0.01442 and 98.558% becomes 0.98558.
4. Calculate the weighted average of the atomic masses using the formula: (fraction of 6Li * atomic mass of 6Li) + (fraction of 7Li * atomic mass of 7Li).
5. Substitute the values into the formula: (0.01442 * 6.015122 u) + (0.98558 * 7.016004 u).

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, lithium has two stable isotopes: 6Li and 7Li. Understanding isotopes is crucial for calculating average atomic weights, as the proportion of each isotope in a sample affects the overall mass.

Average Atomic Weight

The average atomic weight of an element is calculated by taking the weighted average of the atomic masses of its isotopes, based on their natural abundance. This involves multiplying the atomic mass of each isotope by its relative abundance (expressed as a fraction) and summing these products. This concept is essential for determining the average atomic weight of a sample containing multiple isotopes.

Percentage Composition

Percentage composition refers to the proportion of each component in a mixture or compound, expressed as a percentage. In the context of isotopes, it indicates how much of each isotope is present in a sample. For the lithium sample in the question, knowing the percentage of 6Li allows for accurate calculations of the average atomic weight when combined with the atomic masses of the isotopes.