Question

Copper has two naturally occurring isotopes, 63Cu (isotopic mass 62.9296 amu) and 65Cu (isotopic mass 64.9278 amu). If copper has an atomic mass of 63.546 amu, what is the percent abundance of each isotope? Report your answer to 5 significant figures.

Answer 1

Answer:

Percentage of first isotope = 69.152 %

Percentage of second isotope =  30.848 %

Explanation:

The formula for the calculation of the average atomic mass is:

$Average\ atomic\ mass=(\frac {\%\ of\ the\ first\ isotope}{100}\times {Mass\ of\ the\ first\ isotope})+(\frac {\%\ of\ the\ second\ isotope}{100}\times {Mass\ of\ the\ second\ isotope})$

Given that:

For first isotope:

Let % = x %

Mass = 62.9296 amu

For second isotope:

% = 100 - x  %  (Since, there are only two isotopes)

Mass = 64.9278 amu

Average mass = 63.546 amu

Thus,  

$63.546=\frac {x}{100}\times {62.9296}+\frac {(100-x)}{100}\times {64.9278}$

Solving,

1.9982 x = 138.18

Thus,

Percentage of first isotope = x = 69.152 %

Percentage of second isotope = 100 - x % = 30.848 %

Answer 2

The percent abundance of each isotope is

Percentage of first isotope = 75%

Percentage of second isotope =  25%

What is an isotope?

Isotopes are members of an element's family who have the same number of protons but differ in the number of neutrons.

Calculation:

Given, Isotopic mass of 63Cu is  62.9296

Isotopic mass of 65Cu is 64.9278

Atomic mass of Cu is 63.546 amu

Let mass % of  63u Cu is $x$ %

Mass % of 65u Cu  is (100 - $x$ )%

Step 1: Calculating average atomic mass

Average atomic mass =

$\bold{63.5 = \dfrac{\it x}{100} \times 63 + \dfrac{100-\it x}{100}\times65}$

$\bold{63.5 = \dfrac{63\it x}{100} + 65 - \frac{65\it x}{100} =\dfrac{-2}{100} +65}$

$\bold{-1.5 = \dfrac{-2}{100}}$

$\bold{\it x= \dfrac{150}{2} = 75\%}$

So, The percentage abundance of 63u Cu is 75%.  

Now, the percentage abundance of 65 Cu is (100- 75) = 25%

Thus, the percentage of first isotope is 75% and of second is 25%.

Learn more about isotopes, here:

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