Lithium has only two naturally occurring isotopes. The mass of lithium-6 is 6.01512 amu and the mass of lithium-7 is 7.01601 amu. Calculate the relative abundances of the two isotopes.
Hey guys, in this question we talk about the 2 isotopes of Lithium and ask to find their relative abundances, so here let me take myself out of the image so we can work on the question, so there are 2 types of Lithium that naturally occur, there is Lithium 6 which has a mass of 6.05, 6.01512 AMU and then there's Lithium 7 which has a mass of 7.01601 AMU, now remember the formula we're going to use here is atomic mass or average mass, so remember atomic mass is the average mass of the isotopes equals mass of isotope 1 times the fractional abundance of that isotope plus we're going to just say mass of isotope 2 which I abbreviate as MI2 times it's times in fractional abundance so abbreviation FA, so where do we get the atomic mass or average mass? We get that from the periodic table on the periodic table at 6.941 the mass of the first isotope is 6.01512, we don't know it's fractional abundance so it's X plus the mass of the second isotope. Now here's the thing you're going to say that both of these isotopes together represent 100 percent of all the Lithium in the world, remember fractional abundance is your percentage divided by 100 so the total fractional abundance 1, we already figured out that the first isotope is X so the second isotope must be 1-X, It's the remainder that's left over all we have to do now is solve for X so we're going to distribute distribute distribute so that gives me 6.941 equals 6.01512X plus 7.01601 minus 7.01601X, both of these have X in them so they combined together when they combine together they give us -1.00089X + 7.01601 and still equal to the average atomic mass here subtract this this number here for both sides this gets cancelled out so what we'll have here is we'll have -0.07501 = - 1.00089X divide both sides
by this and X here will equal 0.0749. Now this is your fractional abundance we want a relative or percent abundance so we multiply it by 100 so it's 7.49 percent and since this is X it represents the percent or relative abundance of the first isotope so this is the relative abundance of Lithium 6, so how do we figure out the relative or percent abundance of the second isotope? Well together they represent 100 percent so just subtract it from 100 percent so you'll have 92.51 percent as the relative or percent abundance of Lithium 7. So, these would be the 2 percentages or relative abundance of both of the isotopes of Lithium.