URANIUM: A RADIOACTIVE CLOCK

How old is the Earth, the solar system, or a piece of charcoal from an ancient campfire? Until the beginning of the 20th Century, geologists had no method by which to determine the absolute age of a material. The age of the earth was believed to be at most tens of millions of years. Not long after the discovery of radioactivity in 1896, scientists realized that radioactive decay constitutes a “clock” capable of measuring absolute geologic time. By 1907, the discovery that lead was the final product of uranium decay provided evidence that geologic age needed to be reckoned not in millions, but in billions of years.

Uranium
occurs in numerous minerals, such as pitchblende (UO_{3}·UO_{2}·PbO)
and carnotite (K_{2}O·2U_{2}O_{3}·V_{2}O_{5}·3H_{2}O). It is not all that
rare, being more plentiful in the Earth's crust than mercury or silver. The
metal was first isolated in 1841 by the reduction of uranium(IV) chloride with
potassium.

4 K + UCl_{4}
4 KCl + U

Uranium is sufficiently radioactive to expose a photographic plate in about an hour. Naturally occurring U contains 14 isotopes, all of which are radioactive. The three most abundant are U-238 (99.28%), U-235 (0.71%), and U-234 (0.006%). In contrast to chemical reactions, where the isotopes of an element behave similarly, in nuclear reactions isotopes behave quite differently. This reveals itself in the different half lives of these isotopes, and in the fact that among these three only U-235 undergoes fission.

The
most abundant of the naturally occurring uranium isotopes decays by alpha emission
to Th-234

238 | U | 234 | Th + |
4 | He | t_{½} = 4.5 × 10^{9}
years |
||

92 | 90 | 2 |

The product of this reaction, Th-234, is also radioactive and undergoes beta decay.

234 | Th | 234 | Pa + |
0 | e | t_{½} = 24 days |
||

90 | 91 | -1 |

Protactinium-234
also decays by emitting a ß particle. These are only the beginning of
a series of 14 nuclear decay steps. After emission of eight a particles and
six ß particles, the isotope Pb-206 is produced. It is a stable isotope
that does not disintegrate further. The complete process is called the uranium
radioactive decay series. The intermediate isotopes are called “daughters.”
The half lives of the daughters range from 1.6 × 10^{-4} seconds
for Po-214 to 2.5 × 10^{5} years for U-234. Two other such radioactive
series occur in nature. They start with U-235 and Th-232.

The
uranium radioactive series has been used to estimate the age of the oldest rocks
in the Earth's crust. The ratio of U-238 to Pb-206 in a rock changes slowly
as the U-238 in the rock decays. Because the half life of U-238 is 20,000 times
that of the next longest half life in the series, the rate of decay of U-238
is the rate-determining step in the conversion of U-238 to Pb-206. The rate
of radioactive decay is first order in the amount of decaying isotope. Therefore,
the first order equation relates the amount of isotope in a sample to time.

log |
N _{0} |
= |
lamda *t |

N |
2.3 |

In
this equation, N_{0} is the number of U-238 atoms initially present
in the sample, N is the number of U-238 atoms in the sample after a length
of time t has elapsed, and lamda is the decay constant of U-238. If no Pb-206
was initially present in the sample, then N_{0} is equal to the sum
of the number of atoms of U-238 and Pb-206.

At least two other radioactive clocks are used for dating geological time spans. These are the potassium to argon and rubidium to strontium transformations. Potassium-40 decays by electron capture to argon

40 | K | + | 0 | e |
40 | Ar | t_{½} = 1.3 × 10^{9}
years |
||

19 | -1 | 18 |

The other is rubidium-87 which emits a beta particle to form Sr-87.

87 | Rb | 87 | Sr + |
0 | e | t_{½} = 5.7 × 10^{10}
years |
||

37 | 38 | -1 |

These radioactive clocks are more useful for dating rock samples than the uranium clock because both potassium and rubidium are more widely distributed in rock samples than is uranium.

All radiochemical methods of dating have some uncertainties associated with them. Several assumptions must be made in determining an age. Perhaps the most significant assumption is the supposition that the sample was a closed system throughout its existence, that is, no parent or daughter isotope was gained or lost. Another assumption involves the amount of daughter isotope present at the formation of the sample. Generally, this is taken as zero for rare isotopes. The strongest evidence for the age of a sample is obtained when two different radiochemical dating methods produce the same result. Because the chemical properties of daughter products are so very different, any geological transformation of a rock sample will have quite different effects on the sample's daughter isotope contents. Potassium and rubidium frequently occur together in rock samples, making this pair particularly important for radiochemical dating.

Radiochemical dating of samples from the Earth's crust yield a maximum age of
about 3.5 × 10^{9} years. The Earth is believed to be older than
this. The oldest meteorites and moon rocks are 4.5 × 10^{9} years
old. If these other members of the solar system were formed at the same time,
then perhaps the Earth itself was formed 4.5 billion years ago. The isotopic
composition of lead supports this conclusion. Of the four lead isotopes, only
Pb-204 is not produced by radioactive decay of parent U-328, U-235, or Th-232.
Comparing the isotopic composition of lead in the Earth's crust to that of meteorites
free of uranium and thorium indicates that about 4.5 billion years of U and
Th decay would be required to produce the Pb isotope ratios found on Earth.