Answer to Question #147431 in General Chemistry for Galata

Question

Lithium has two naturally occurring isotopes: lithium-6 and lithium-7. If the average atomic mass of lithium is 6.941 atomic mass units, which isotope is the most abundant? How do you know?

Answer 1

Let $w(isotope)$ stand for the ratio of the overall amount of that isotope to the overall amount of all isotopes of the specified element.

Then for $Li$ the following holds:

$w(^6Li) + w(^7Li) = 1$

and

$6*w(^6Li) + 7*w(^7Li) = 6.941$

From the first equation:

$w(^6Li) = 1 - w(^7Li)$

From this and the second equation:

$6*(1 - w(^7Li)) + 7*w(^7Li) = 6.941$

$6 - 6* w(^7Li) + 7*w(^7Li) = 6.941$

$w(^7Li) = 0.941$

$w(^6Li) = 0.059$

$w(^6Li) < w(^7Li)$ , therefore $^7Li$ is the most abundant isotope.

Answer: $^7Li$ is the most abundant isotope