# Question #b220e

##### 1 Answer

Here's what I got.

#### Explanation:

You can find the *average atomic mass* of copper,

The average atomic mass is added at the **bottom** of the element box; in copper's case, you have an average atomic mass of

Now, the average atomic mass of a given element is calculated by taking the **weighted average** of the atomic masses of its stable isotopes.

The *weighted average* refers to the fact that the **abundance** of each isotope determines its contribution to the average atomic mass of the element.

#color(blue)(ul(color(black)("avg. atomic mass" =))) sum_icolor(blue)(ul(color(black)( "isotope"_i xx "abundance"_i)))#

Keep in mind that the above equation uses **decimal abundance**, which is simply percent abundance divided by

So, you know that copper has two stable isotopes and that copper-63 has an abundance of

#69.17% = (69.17color(red)(cancel(color(black)(%))))/(100color(red)(cancel(color(black)(%)))) = 0.6917#

This means that the second isotope will have an abundance of

#100% - 69.17% = 30.83% = (30.83 color(red)(cancel(color(black)(%))))/(100color(red)(cancel(color(black)(%)))) = 0.3083#

If you take

#"63.546 u" = x * 0.3083 + "62.939 u" * 0.6917#

Rearrange to solve for

#x = ("63.546 u " - " 43.535 u")/0.3083 = color(darkgreen)(ul(color(black)("64.908 u")))#

I'll leave the answer rounded to five **sig figs**.

To find the **identity** of the second isotope, i.e. its *mass number*, round the atomic mass to the **nearest whole number**. In this case, you have

#64.908 ~~ 65#

The second isotope is *copper-65*, or