The atomic masses of \({ }_{3}^{6} \mathrm{Li}\) and \({ }_{3}^{7} \mathrm{Li}\) are \(6.0151 \mathrm{amu}\) and 7.0160 amu, respectively. Calculate the natural abundances of these two isotopes. The average atomic mass of Li is 6.941 amu.

The atomic mass unit (amu) is a standardized unit of mass that is used to express the mass of atoms or molecules. It is defined as one twelfth of the mass of a carbon-12 atom, where the carbon-12 atom has 6 protons and 6 neutrons. In other terms, 1 amu is equivalent to approximately 1.660539 × 10^-24 grams.

Understanding amu is crucial when studying atomic masses and comparing the weights of different isotopes, as the differences in atomic masses among isotopes are usually very small and are best described using this unit. For example, in the exercise provided, lithium's isotopes have atomic masses of 6.0151 amu and 7.0160 amu, showing the precision necessary for isotopic measurements.

Natural isotopic abundance refers to the relative proportion of isotopes of a given element found in nature. It is commonly expressed as a percentage that indicates how much of an element's total natural occurrence is made up of a particular isotope. Since elements naturally occur as a blend of different isotopes, understanding isotopic abundance is key to determining the average atomic mass of an element.

For example, in the exercise, you would calculate the natural abundances of lithium's isotopes (\( ^6Li \) and \( ^7Li \) ) to determine how much each isotope contributes to lithium's average atomic mass. The isotopes' abundances are important for various applications, including nuclear medicine and radiometric dating.

The average atomic mass is the weighted average of the atomic masses of the naturally occurring isotopes of an element. This factor considers both the mass and the natural abundance of each isotope. It is important to note that the average atomic mass is not just an arithmetic mean but a value that reflects isotopic abundances as they are found in nature.

To calculate the average atomic mass, one multiplies the atomic mass of each isotope by its natural abundance (as a decimal) and then sums these products. This is exemplified in the given exercise where you are solving for the average atomic mass of lithium, using the equation based on mass and abundance of its isotopes to arrive at the known average atomic mass of 6.941 amu.

Lithium, like all elements, consists of atoms with the same number of protons but different numbers of neutrons. These variants are called isotopes. The most common isotopes of lithium are lithium-6 (\( ^6Li \) ) with 3 protons and 3 neutrons, and lithium-7 (\( ^7Li \) ) with 3 protons and 4 neutrons. The atomic number, which is 3 for lithium, remains constant across isotopes since it is defined by the number of protons.

\( ^6Li \) and \( ^7Li \) differ slightly in mass due to the additional neutron in \( ^7Li \) , but they also differ in their natural isotopic abundance, which affects how the average atomic mass of natural lithium is calculated. This distinction in isotopes and their unique abundances are central to the exercises that aim to determine the natural abundances of lithium's isotopes from their average atomic mass.