## Q. 3.3

Naturally occurring chlorine exists in two isotopic forms, $^{35}_{17}$Cl and $_{17}^{37}$Cl. The relative mass of $^{35}_{17}$Cl is 34.97 amu, and its abundance is 75.53%; the relative mass of $^{37}_{17}$Cl is 36.97 amu, and its abundance is 24.47%. What is the atomic mass of chlorine?

## Verified Solution

An element’s atomic mass is calculated by multiplying the relative mass of each isotope by its fractional abundance and then totaling the products. The fractional abundance for an isotope is its percentage abundance converted to decimal form (divided by 100).
$\quad ^{35}_{17}Cl:\quad\quad (\frac{75.53}{100})\times 34.97 amu=(0.7553)\times34.97 amu=26.41 amu$
$\quad ^{37}_{17}Cl:\quad\quad (\frac{24.47}{100})\times 36.97 amu=(0.2447)\times36.97 amu=9.047 amu$

$\quad\quad$ Atomic mass of Cl = (26.41 + 9.047) amu

$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$= 35.46 amu

$\quad\quad$This calculation involved an element containing just two isotopes. A similar calculation for an element having three isotopes would be carried out the same way, but it would have three terms in the fi nal sum; an element possessing four isotopes would have four terms in the fi nal sum.