Question

Thallium has two stable isotopes, ²⁰³TI and ²⁰⁵TI. Knowing that the atomic weight of thallium is 204.4, which isotopes is the more abundant of the two?

Answer 1

To determine which isotope of thallium is more abundant, we can use the concept of weighted averages based on the atomic mass of the element.

Thallium has two stable isotopes:
- \(^{203}\text{Tl}\) with an atomic mass of approximately 203 amu
- \(^{205}\text{Tl}\) with an atomic mass of approximately 205 amu

The average atomic mass of thallium is given as 204.4. We can use this information to set up the calculation.

Let:
- \(x\) be the abundance of \(^{203}\text{Tl}\)
- \(1 - x\) be the abundance of \(^{205}\text{Tl}\)

Then we can set up the equation for the weighted average:

\[
204.4 = 203x + 205(1 - x)
\]

Expanding the right side:
\[
204.4 = 203x + 205 - 205x
\]
\[
204.4 = 205 - 2x
\]

Now, solving for \(x\):
\[
2x = 205 - 204.4
\]
\[
2x = 0.6
\]
\[
x = 0.3
\]

So, the abundance of \(^{203}\text{Tl}\) is 0.3 or 30%, and the abundance of \(^{205}\text{Tl}\) is \(1 - 0.3 = 0.7\) or 70%.

Thus, \(^{205}\text{Tl}\) is the more abundant isotope of thallium.