The element lithium has two common isotopes: Li–6 and Li–7 If the average atomic mass of lithium is 6.94004 u, determine its percent isotopic abundances. Step by step and explain.

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Explanation:

First we need to determine the average atomic mass of these isotopes.

The atomic masses of Lithium-6 and Lithium-7 are 6.0151amu and 7.0160amu respectively.

Now that we have that, we need to set up the relative abundance problem.

We can do that using the formula (M1)(x) + (M2)(1-x) = M(E)

Because you asked for details, I'll explain what each variable stands for-

M1 = the mass of one isotope

x = the relative abundance

M2 = the mass of the second isotope

M(E) = the atomic mass of the element from the periodic table

Therefor all we do now is plug in our respective variable.

M1 = 6.0151amu (Lithium-6)

x = unknown relative abundance

M2 = 7.0160amu (Lithium-7)

M(E) = 6.94004amu

Now the formula plugged in will look like this:

6.0151x + 7.0160(1-x) = 6.94004

Now doing some quick math, we can determine that x=0.07589

For the last step we need to find the percent abundance of each element, which is quite simple. We take X and multiply it by 100 to find Lithium-6, so 0.076 x 100 = 7.6%

and since then we use 1 - X, so 1 - 0.076 = 0.924

We take that and also multiply it by 100, so 0.924 x 100 = 92.4%

Conclusion:

The abundance of the Lithium-6 isotope is 7.6%, and the abundance of the Lithium-7 isotope is 92.4%.

Please ask if you have any questions and I hope this was helpful!

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