Chemistry

Problem

Tin (Sn) has two principal isotopes,

^{116}\text{Sn}

and

^{118}\text{Sn}

. A naturally occurring ore sample contains tin in which the ratio of

^{116}\text{Sn}

atoms to

^{118}\text{Sn}

atoms is 1.350 : 1.000. The measured average atomic mass of tin in this ore is 117.20 amu. (a) Express the percent abundance of each isotope in terms of a single unknown variable. (b) Using the information provided, determine the percent abundance of

^{116}\text{Sn}

and of

^{118}\text{Sn}

. Show all algebraic steps. (c) Evaluate whether the calculated average atomic mass for your percent abundances would change if the ore contained trace amounts (

<0.10\,\%

) of

^{120}\text{Sn}

. Justify your answer quantitatively. a. Part (a) – Define the unknowns. b. Part (b) – Calculate the abundances. c. Part (c) – Assess the impact of a trace isotope.

Intuitive explanation

The key to isotope problems is recognizing that percent abundances must sum to 100%, and the weighted average of isotope masses equals the measured atomic mass. Here, you're given a ratio of atoms rather than percentages directly—so set up one variable for abundance and use the constraint that both isotopes account for all the tin to build an equation. Once you solve for abundances, you can test whether a tiny third isotope would meaningfully shift the average.

Intuitive explanation

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