Thallium has two stable isotopes, 203tl and 205tl. knowing that the atomic weight of thallium is 204.4, which isotope is the more abundant of the two? explanation

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Chemistry

Zion Haley

3 April, 05:55

Thallium has two stable isotopes, 203tl and 205tl. knowing that the atomic weight of thallium is 204.4, which isotope is the more abundant of the two? explanation

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Marin Rich · Answer 1

You have to figure out a way to write the two unknown abundances in terms of one variable.

The total abundance is 1 (or 100%). So if you say the abundance for the first one is X then the abundance for the second one has to be 1-X (where X is the decimal of the percentage so say 0.8 for 80%).

203 (X) + 205 (1-X) = 204.4

Then you just solve for X to get the percentage for TI-203.

And then solve for 1-X to get the percentage for TI-205.

After that the higher percentage would be the most abundant.

203x + 205 - 205x = 204.4

-2x + 205 = 204.4

-2x = - 0.6

x = 0.3

1-x = 0.7

Then the TI-205 would have the highest percentage and would be the most abundant.