Why do nuclei like Uranium and Thorium have such long half lives?

[iced199]

Why is it that those atoms, with atomic numbers of 90 and 92 have much, much longer half lives than atoms like Radon, Radium, and Polonium? I do realize that atoms with even atomic numbers are more stable than ones with odd numbers, so it makes sense why atoms like astatine, actinium, and francium are really unstable, but why do elements 90 and 92 have half lives in the billions of years? No other unstable element, besides bismuth (but its really close to lead, so it makes sense why its almost stable) have such extraordinary lives. It seems like these two elements have some kind of a boost in stability - they don't follow the general trend towards instability at all.

 

[mfb]

There are many isotopes with lifetimes of billion of years or even more.
If you compare isotopes with other isotopes nearby, nuclear shell effects become relevant.

 

[Bill_K]

One feature of α decay is so striking that it was noticed as long ago as 1911. Geiger and Nuttall noticed that α emitters with large disintegration energies had short half-lives and conversely. The variation is astonishingly rapid. A factor of 2 in energy means a factor of 10²⁴ in half-life! The theoretical explanation of this rule in 1920 was one of the first triumphs of quantum mechanics.

For more details, see the Wikipedia page on this.

 

[iced199]

I'm mainly talking about the general trend of half lives shortening in elements heavier than lead. They all decrease in a curve, with the exception of uranium and thorium. They're outliers. Why?

 

[Bill_K]

They're outliers. Why?

No, they're not outliers. But they are an extreme case. If you use the semi-empirical mass formula, you see a well-known trend, that in this part of the table, binding energies fall off with increasing A. As a result, Th-232 and U-238 have Q ≈ 4 MeV for alpha decay, and by the Geiger-Nuttall rule this implies a very long half-life. Beyond Uranium, nuclei are unstable for other decays such as fission, so U and Th are the last cases where the α-decay half-life dominates.

 

[mfb]

Beyond Uranium, nuclei are unstable for other decays such as fission, so U and Th are the last cases where the α-decay half-life dominates.

Most (or at least many, did not count all of them) transuranium element isotopes have alpha and beta decays as dominant modes.

I'm mainly talking about the general trend of half lives shortening in elements heavier than lead.

That is a general trend beyond uranium (and might be wrong if there is an island of stability beyond Z=118), but not between uranium and lead, see the chart of nuclides, for example.

 

[Bill_K]

Beyond Uranium, nuclei are unstable for other decays such as fission, so U and Th are the last cases where the α-decay half-life dominates.

Most (or at least many, did not count all of them) transuranium element isotopes have alpha and beta decays as dominant modes.

True, but misleading. The issue is, which isotopes? Here's a list of approximate half-lives:

Th-228 1 y
Th-230 10⁴ y
Th-232 10¹⁰ y
Th-234 rapid β decay

U-234 10⁵ y
U-236 10⁷ y
U-238 10⁹ y
U-240 rapid β decay

Pu-238 10² y
Pu-240 10⁴ y
Pu-242 10⁵ y
Pu-244 rapid β decay

My point is that Pu-244 and Pu-246 would have continued the long half-life trend, but the β decay instability took over.

 

[snorkack]

Pu-242 10⁵ y
Pu-244 rapid β decay

My point is that Pu-244 and Pu-246 would have continued the long half-life trend, but the β decay instability took over.

Manifestly false!
Pu-244 10⁸ y!

Pu-246 does have rapid beta decay (10 days)

But elements 90 and 92 are not "outliers". They are the tip of a sizable maximum.

Looking at even elements:
82 - stable
84 - 103 years
86 - 3,8 days

but that was the minimum, next

88 - 1600 years
90 - 14 milliard years
92 - 4,5 milliard years

But the maximum goes on:

94 - 82 million years
96 - 16 million years

Then falling deeper:
98 - 900 years (still longer than 84)
100 - 100 days - but existence of other isotopes possible

Odd elements have a similar pattern:

81 - stable
83 - 10¹⁹ years
85 - 8 hours
87 - 22 minutes

And again a rise to a maximum:

89 - 21 years
91 - 32 000 years
93 - 2,1 million years

And then a (slower) fall:

95 - 7400 years
97 - 1400 years
99 - 470 days

 

[Bill_K]

Pu-244 rapid β decay

Manifestly false! Pu-244 10⁸ y!

Sorry Snorkack, I stand corrected. I hope I didn't upset you too much.