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Chapter 3: Problem 128

Naturally occurring copper, \(\mathrm{Cu}\), is composed of two isotopes. The isotope copper-63 is \(69.17 \%\) of naturally occurring copper and has an atomic mass of \(62.94\) amu. The isotope copper- 65 has an atomic mass of \(64.93\) amu. (a) What percent of naturally occurring copper is copper-65? (b) Calculate the atomic mass of naturally occurring copper.

Short Answer

Expert verified
The percentage of naturally occurring copper that is copper-65 is \(30.83 \%\), and the atomic mass of naturally occurring copper is approximately \(63.55 \, \text{amu}\).

Step by step solution

01

Determine the percentage of copper-65

Since we know that copper-63 makes up \(69.17 \%\) of naturally occurring copper, we can simply subtract this percentage from \(100 \%\) to find the percentage of copper-65. $$ \text{Percentage of copper-65} = 100 \% - \text{Percentage of copper-63} $$
02

Calculate the percentage of copper-65

Following the formula for the percentage of copper-65 from Step 1, we plug in the given value for copper-63. $$ \text{Percentage of copper-65} = 100 \% - 69.17 \% = 30.83 \% $$
03

Calculate the weighted average atomic mass of naturally occurring copper

To find the atomic mass of naturally occurring copper, we need to take the weighted average of the atomic masses of its isotopes. This can be found using the formula: $$ \text{Atomic mass of copper} = (\text{Percentage of copper-63} \times \text{Atomic mass of copper-63}) + (\text{Percentage of copper-65} \times \text{Atomic mass of copper-65}) $$
04

Find the atomic mass of naturally occurring copper

Using the values given in the problem and the percentage of copper-65 found in Step 2, we can find the atomic mass of naturally occurring copper. $$ \text{Atomic mass of copper} = (69.17 \% \times 62.94 \, \text{amu}) + (30.83 \% \times 64.93 \, \text{amu}) $$ Convert percentages to decimals by dividing by 100. $$ \text{Atomic mass of copper} = (0.6917 \times 62.94 \, \text{amu}) + (0.3083 \times 64.93 \, \text{amu}) $$ Now perform the multiplication and addition. $$ \text{Atomic mass of copper} = 43.534978 \, \text{amu} + 20.018179 \, \text{amu} = 63.553157 \, \text{amu} $$ The atomic mass of naturally occurring copper is approximately \(63.55 \, \text{amu}\).

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Most popular questions from this chapter

Bromine exists as only two isotopes in nature, \({ }_{35}^{79} \mathrm{Br}\) (atomic mass \(78.918336\) amu, \% natural abundance \(=50.69 \%\) and \({ }_{35}^{81}\) Br (atomic mass \(80.916289\) amu). (a) What is the percent natural abundance for \({ }_{35}^{81} \mathrm{Br}\) ? (b) Calculate the atomic mass of the naturally occurring mixture of isotopes.

Write the name of each element: (a) \(\mathrm{Be}\) (b) \(\mathrm{Mg}\) (c) \(\mathrm{Fe}\) (d) \(S\) (e) \(\mathrm{Ar}\) (f) \(\mathrm{Cu}\)

Naturally occurring hydrogen on Earth has an atomic mass of \(1.0079\) amu. Suppose you were on another planet and found the atomic mass of hydrogen to be \(1.2000\) amu. How would you explain this? (The atomic mass of \({ }_{1}^{1} \mathrm{H}\) is \(1.0078252\) amu; the atomic mass of \({ }_{1}^{2} \mathrm{H}\) is \(2.1041022\) amu.)

What is the identity of element \(X\) if its \(2+\) cation contains ten electrons?

How much more massive is an "average" oxygen atom than \(\mathrm{a}_{6}^{12} \mathrm{C}\) atom? (Use the periodic table for the atomic mass of oxygen.)
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