The atomic weight of copper is 63.546 amu. The two naturally...

The atomic weight of copper is 63.546 amu. The two naturally occurring isotopes of copper have the following masses: ${ }^{63} \mathrm{Cu}, 62.9298 \mathrm{amu} ;{ }^{65} \mathrm{Cu}, 64.9278$ amu. Calculate the percent of ${ }^{63} \mathrm{Cu}$ in naturally occurring copper.

Key Concepts

Percent Abundance Calculation

Percent abundance calculation is the process used to determine the percentage of a specific isotope in a naturally occurring element. It involves setting up an equation that relates the known atomic weight to the isotopic masses and solving for the fraction or percentage of the target isotope.

Weighted Average Calculation

Weighted average calculation involves multiplying the mass of each isotope by its relative abundance and summing these products to obtain the overall atomic weight of the element. This method allows for the determination of individual isotopic abundances when the average atomic weight and isotopic masses are known.

Isotopes

Isotopes are forms of the same element that differ in neutron number and therefore in mass. They are chemically similar but vary in their nuclear properties and mass numbers, leading to different contributions in the weighted average calculation.

Atomic Weight

Atomic weight represents the average mass of an element's atoms as found in nature, taking into account the relative abundances of its isotopes. It is calculated as the weighted average of all isotopic masses present in a natural sample.

Transcript

00:01 Hi, we will be looking together at question number 32.

00:07 In question number 32, we are interested in what percent of a sample of copper is due to the isotope copper 63.

00:20 There are only two isotopes that make up copper, two naturally occurring isotopes, copper 63 and copper 65.

00:28 So the atomic weight of copper, which is 63 .546, is due to a weighted average based upon the two isotopes and their percent abundance.

00:49 So we need to figure out, we do have the masses of each of the isotopes, but we need to figure out their abundance, the percent abundance.

01:00 So we are going to let copper 63 equal x.

01:07 And since there are only two isotopes, if the fraction of the sample that is copper 63 is x, then the fraction of the sample that will be due to copper 65 will be 1 minus x.

01:24 Because when we put the two together, we should get 100 % or 1.

01:28 So we can now set up an equation where we can take the weight of the copper 603, times x plus the weight of the copper 65 times one minus x is equal to the atomic weight.

01:42 So let's go ahead and do that.

01:43 Let's set that up and then solve for x.

01:47 So copper 63 has a weight of 62 .9298 am u.

01:58 Multiply that times x because that is the abundance of copper 63.

02:05 And then we're going to add that because this is a weighted average.

02:10 So we're going to take the mass of the copper 65 times one minus x...

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