Naturally occurring iodine has an atomic mass of 126.9045 amu. \(\mathrm{A} 12.3849 \mathrm{~g}\) sample of iodine is accidentally contaminated with an additional \(1.00070 \mathrm{~g}\) of \({ }^{129} \mathrm{I}\), a synthetic radioisotope of iodine used in the treatment of certain diseases of the thyroid gland. The mass of \({ }^{129} \mathrm{I}\) is 128.9050 amu. Find the apparent "atomic mass" of the contaminated iodine.

Isotope contamination occurs when a sample of a particular element is mixed with isotopes other than those naturally or commonly found. In our case, naturally occurring iodine, which has an atomic mass of 126.9045 amu, is contaminated with an extra gram of the synthetic radioisotope I-129, commonly used in medicine. This contamination changes the average atomic mass of the iodine sample.

To understand the impact of such contamination, one must consider the atomic mass and the number of moles of each isotope present. The average atomic mass of a sample is calculated by summing the products of the mass and relative abundance of each isotope. Contamination skews this average as it adds additional mass from an external source, thereby altering the mass-to-isotope ratio.

The mole concept is a foundational idea in chemistry that connects the microscopic world of atoms to the macroscopic world we can measure. A mole represents Avogadro's number (\(6.022 \times 10^{23}\) particles) and is used to count atoms, ions, or molecules in a given sample.

When calculating the effects of isotope contamination, the mole concept allows us to transition from the mass of our samples in grams to the number of atoms present. By dividing the mass of each iodine sample (both natural and contaminated) by its atomic mass, we determine the number of moles, which, in turn, is crucial for finding the apparent atomic mass after contamination. Clearly understanding how many moles of each isotope are present is essential for accurate atomic mass calculation.

An atomic mass unit (amu) is a standard unit of mass that quantifies the mass of atoms or molecules on a scale suited for particles of such a small scale. It is defined as one-twelfth of the mass of a carbon-12 atom, which has six protons and six neutrons.

The significance of the amu becomes evident when we need to compare the masses of different atoms, such as in the contamination problem. Here, we deal with iodine and its radioisotope, I-129, which have slightly different masses expressed in amu. Precise knowledge of these masses is imperative for calculating the mole ratio and subsequently, the new average atomic mass after contamination.

Radioisotopes are isotopes that emit radiation and are frequently used in medicine, both for diagnostic and treatment purposes. For example, I-129, the contaminant in our exercise, is a radioisotope used in certain treatments for thyroid diseases. It's chosen due to its radiation properties, which can be detected by medical equipment or can target diseased cells.

Incorporating radioisotopes into medical practice requires careful calculation and understanding of their physical and chemical properties. This extends to their atomic mass, as knowing this helps in dosing the correct amount of a radioactive substance for a patient. The application of these calculations shows the practical importance of precise atomic mass determination for radioisotopes.

Stoichiometry is the section of chemistry that involves using balanced chemical equations to calculate the relative quantities of reactants and products involved in chemical reactions. It relates to the mole concept and atomic masses because these are the parameters we use to ensure a reaction goes to completion and to predict the amount of product formed.

In the context of isotope contamination, stoichiometry can help us understand how the addition of extra mass affects the reaction quantities and the final product. By knowing the stoichiometric ratios, we can predict the change in the average atomic mass of a contaminated element, as is required for the exercise's solution. Proper stoichiometric calculations ensure that changes in composition due to contamination are accurately reflected in the apparent atomic mass.