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Wikipedia says that the half-life of Uranium-$235$ is $7.038 \times 10^8$ ($\text{703 800 000}$) years.

This is very long. Therefore, on a human time scale, the decay is very small, posing difficulty for determining the half-life.

So Who and how was the half-life calculated?

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    $\begingroup$ Identical to physics.stackexchange.com/questions/7584/… $\endgroup$ – user108787 Jun 4 '16 at 14:54
  • $\begingroup$ There is some overlap, but not the same question, I would say. $\endgroup$ – poisson Jun 4 '16 at 15:06
  • $\begingroup$ As in "Who did It", that's fair enough, (if you mean" Who first measured it" but the very best of luck to you in your Googling, I looked and could not find out. I would guess the technique dates to the time of the Curies, Becquerel and Rutherford. $\endgroup$ – user108787 Jun 4 '16 at 15:15
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    $\begingroup$ Call the half life a billion years. That is about 3E16 seconds. One mole of atoms is 6E23. So, about 3,000,000 atoms would decay per second. $\endgroup$ – Jon Custer Jun 4 '16 at 15:22
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    $\begingroup$ For the extreme, Bi-209 has a half-life of 2 x 10E19 years! $\endgroup$ – DJohnM Jun 4 '16 at 19:04
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The earliest reference I've been able to find on the half-life of 235U is in The Uranium Half-Lives: A Critical Review, by Norman Holden, which reviews various early studies of each of the common isotopes of uranium (232U, 233U, 234U, 235U, 236U, and 238U). The earliest study he cites is Nier (1939) (A. 0. Nier, The isotopic constitution of uranium and the half-lives of the uranium isotopes, Phys. Rev. 55 150 (1939))1.

Nier looked at ratio of 206Pb to 207Pb in 21 samples of radiogenic lead - that is, lead that has been formed by radioactive decay, in this case, from Uranium. 206Pb is a decay product of 238U, while 207Pb is a decay product of 235U. He then determined that the actinium series - the decay chain of 235U to 207Pb - is 4.6$\pm$0.1% as active as the uranium series - the decay chain of 238U to 206Pb. Then, using the ratio of 238U to 235U in natural samples, he was able to calculate the half-life of 235U. It is not mentioned as to how he was able to calculate the half-life of 238U.

Interestingly enough, Nier's value is closer to the accepted value than the half-lives found in many later studies using $\alpha$-counting, which looked at the number of $\alpha$ particles emitted during the decay of 235U.


1 I was able to find Nier's abstract in Report of the Committee on the Measurement of Geologic Time (pages 45-46).

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