Silver is composed of two naturally occurring isotopes:...

Silver is composed of two naturally occurring isotopes: Ag-107 $(51.839 \%)$ and $\mathrm{Ag}-109 .$ The ratio of the masses of the two isotopes is $1.0187 .$ What is the mass of $\mathrm{Ag}-107 ?$

Key Concepts

Isotopes

Isotopes are atoms of the same element that contain equal numbers of protons but differ in the number of neutrons. This difference in neutron count leads to different masses for each isotope, although their chemical properties remain nearly identical. Understanding isotopes is crucial in fields like chemistry and physics, especially when calculating atomic masses and studying nuclear processes.

Relative Abundance

Relative abundance refers to the percentage or fraction of each isotope present in a naturally occurring sample of an element. This concept is used to determine the average atomic mass of an element by weighting the masses of its isotopes according to their occurrence. It is a key idea in understanding how atomic weights are derived and how they can vary between different samples.

Mass Ratio

A mass ratio is a comparative measure that expresses the mass of one isotope relative to another. It provides a relationship between the two isotopic masses and is used in conjunction with relative abundances to deduce unknown values in isotopic calculations. This ratio is fundamental when setting up equations to solve for one mass given a known relationship to another.

Weighted Average Atomic Mass

The weighted average atomic mass of an element is calculated by multiplying the mass of each isotope by its relative abundance and then summing the results. This concept bridges the gap between the discreet masses of individual isotopes and the average mass reported on the periodic table. It is an essential tool in analytical chemistry and atomic theory for understanding the overall composition of elements.

Algebraic Problem Solving in Isotopic Calculations

Algebraic problem solving in the context of isotopic calculations involves setting up and solving equations that connect the known and unknown quantities, such as isotopic masses, mass ratios, and relative abundances. This approach enables one to determine unknown isotope masses or abundances by using relationships like ratios and weighted averages.

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