Given that the Earth is around 4.5 billion years old, we would not expect to find any radioactive isotopes with short half-lives in the crust of the Earth as they would have long since decayed away. Conversely, if the Earth really was six thousand years old, then we'd expect to find these short-lived radioactive isotopes as insufficient time would have passed for them to have decayed away. When we examine the Earth's crust to look for short-lived radioactive isotopes, apart from those naturally made, we find no short-lived isotopes, just what we'd expect if the Earth was ancient.
In his book The Age of the Earth [1], respected geologist G. Brent Dalrymple looks at this splendid demonstration of the antiquity of the Earth. He remarks
There are 34 unstable nuclides with half-lives greater than 1 Ma [Table 1]. Of these, 23 are found in nature. Five of the 23, however are continually being produced by natural nuclear reactions...The 17 remaining radioactive nuclides all have half-lives of 82 Ma or more. The absence of short-lived unstable nuclides in nature holds true even if the list in [Table 1] is extended to include nuclides with half-lives less than 1Ma; only those whose existence is due to continual production by natural processes (or in some cases by man) are found. How can this most logically be explained? [2]
Table 1- Known radioactive isotopes with half-lives greater than one million years
|
Nuclide |
Half-Life (Years) |
Found in Nature? |
|
50V |
6x1015 |
yes |
|
144Nd |
2.4x1015 |
yes |
|
174Hf |
2x1015 |
yes |
|
192Pt |
~1x1015 |
yes |
|
115In |
6x1014 |
yes |
|
152Gd |
1.1x1014 |
yes |
|
123Te |
1.2x1013 |
yes |
|
190Pt |
6.9x1011 |
yes |
|
138La |
1.12x1011 |
yes |
|
147Sm |
1.06x1011 |
yes |
|
87Rb |
4.88x1010 |
yes |
|
187Re |
4.3x1010 |
yes |
|
176Lu |
3.5x1010 |
yes |
|
232Th |
1.4x1010 |
yes |
|
238U |
4.47x109 |
yes |
|
40K |
1.25x109 |
yes |
|
235U |
7.04x108 |
yes |
|
244Pu |
8.2x107 |
yes |
|
146Sm |
7x107 |
no |
|
205Pb |
3x107 |
no |
|
236U |
2.39x107 |
yes – naturally made |
|
129I |
1.7x107 |
yes – naturally made |
|
247Cm |
1.6x107 |
no |
|
182Hf |
9x106 |
no |
|
107Pd |
~7x106 |
no |
|
53Mn |
3.7x106 |
yes – naturally made |
|
135Cs |
3x106 |
no |
|
97Tc |
2.6x106 |
no |
|
237Np |
2.14x106 |
yes – naturally made |
|
150Gd |
2.1x106 |
no |
|
10Be |
1.6x106 |
yes – naturally made |
|
93Zr |
1.5x106 |
no |
|
98Tc |
1.5x106 |
no |
|
154Dy |
~1x106 |
no |
Dalrymple advances three hypotheses to explain this:
Dalrymple calculates the odds that purely by chance the Earth's crust has the long-lived isotopes and none of the short-lived isotopes as 1 chance in 9x107. He notes that the odds become even worse when we factor in all the radioactive isotopes with even shorter half-lives. After around 10 half-lives, a radioisotope will have decayed away to an undetectable quantity. If the Earth was - say - ten thousand years old, then we'd expect to be able to detect all the radiioisotopes with half-lives greater than one thousand years. The odds blow out to one chance in 3x1014. As slim as those odds are, Dalrymple notes that the calculations should properly include the 269 stable isotopes found in the crust as well as those radioisotopes with long half-lives. When this is done, the odds that the Earth is young but by chance none of the short-lived radioisotopes are present drop to an improbable 1 chance in 1053. These odds are so small that we can effectively dismiss the chance that the earth really is young but all the short-lived radioisotopes that we'd expect not to have decayed away purely by chance are missing.
What about the possibility that the process that forms elements is incapable of making short-lived radioisotopes? Dalrymple notes [3] that short-lived radioisotopes can be detected in stars. They can also be formed in nuclear reactors. Thus, there seems to be no barrier to the synthesis of short-lived radioisotopes. Therefore, the only credible explanation for why we find no short-lived radioisotopes in the crust of the Earth is that the Earth is old, and all these short-lived isotopes have decayed away. The Earth truly is ancient.
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