Calculating relative atomic mass

The carbon-12 atom, \(_{6}^{12}\textrm{C}\) is the standard atom against which the masses of other atoms are compared. The relative atomic mass of an element is the average mass of its atoms, compared to 1/12th the mass of a carbon-12 atom. The relative atomic mass, Ar, of an element is calculated from:

Chlorine

Chlorine naturally exists as two isotopes, \(_{17}^{35}\textrm{Cl}\) (chlorine-35) and \(_{17}^{37}\textrm{Cl}\) (chlorine-37). The abundance of chlorine-35 is 75% and the abundance of chlorine-37 is 25%. In other words, in every 100 chlorine atoms, 75 atoms have a mass number of 35, and 25 atoms have a mass number of 37.

To calculate the relative atomic mass, Ar, of chlorine:

\[A_{r} = \frac{total~mass~of~atoms}{total~number~of~atoms} = \frac{(75 \times 35)+(25 \times 37)}{(75+25)}\]

\[A_{r} = \frac{2625+925}{100} = \frac{3550}{100}\]

\(A_{r} = 35.5\) (to 1 decimal place)

Notice that the answer is closer to 35 than it is to 37. This is because the chlorine-35 isotope is much more abundant than the chlorine-37 isotope.

Question

The table shows the mass numbers and abundances of naturally occurring copper isotopes.

Mass numberAbundance
6369%
6531%

Calculate the relative atomic mass of copper. Give your answer to 1 decimal place.

\[A_{r} = \frac{(69 \times 63)+(31 \times 65)}{(69+31)}\]

\[A_{r} = \frac{4347+2015}{100} = \frac{6362}{100}\]

\[A_{r} = 63.6\]

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