Grade 6Physical Chemistry

Naturally occurring thallium has two stable isotopes, Tl-203 and Tl-205. If the average atomic mass of thallium is 204.4 a.m.u., determine the percentage abundance of Tl-203.
Anyone can reply me the answer? Thanks!!!!

1 Answer

These always come down to a fairly simple algebra problem:

(Mass 1) * (%abundance of mass 1) + (mass 2) * %(abundance of mass 2) = atomic mass;

So in your case

(203) * (% of 1) + (205) * (% of 2) = 204.4

or
203*x + 205*y = 204.4

But we have x and y, two unknowns with 1 equation only....
but if we know that x and y are the only two (natural) isotopes of thallium then we have a second equation
(% of isotope 1) + (% of isotope 2) = 100%;
x + y = 100%; or y = 100%-x;

So going back to the original problem

203*x + 205*y = 204.4
y becomes (100% - x; or 1-x)

203*x + 205*(1-x) = 204.4, which is solvable.

For a real trick, try finding it for an element with three isotopes
assuming you know the % abundance of one isotope, the masses of all three, the relative atomic mass.