The period 1896-1905 marks the discovery of radioactivity and the realization that rocks could be dated by radioactive decay.
1896 A. Henri Becquerel discovers that uranium-bearing compounds emit invisible rays similar to X-rays. (X-rays had been discovered in 1895 by Wilhelm Roentgen.) 1898 Marie and Pierre Curie coin the term "radioactivity," prove that radioactivity is a property of atoms (as opposed to molecular composition), discover radioactivity of thorium, and identify a few of the intermediate products of the uranium and thorium decay series. 1902 Ernest Rutherford and Frederick Soddy demonstrate the exponential nature of radioactive decay. 1905 In a lecture at Harvard, Ernest Rutherford suggests that uranium/helium or uranium/lead ratios could theoretically be used to compute the age of rocks.
However, this did not prevent geologists from making several uranium/helium and uranium/lead measurements over the next few years. In many cases the work was done on rocks whose relative ages were known independently, in order to assess whether or not the element ratios correlated with relative age. It was discovered that uranium/helium is not generally reliable because helium is not retained consistently.
1907 B.B. Boltwood takes measurements that indicate lead to be a final product of uranium decay, for its abundance is strongly correlated with relative age of uranium-bearing minerals. Boltwood attempts some simple uranium/lead ages, extrapolating the uranium decay rate from the assumption of decay equilibrium and the previously measured radium decay rate. (When a decay series has reached equilibrium, the ratio of the quantity of elements present is equal to the ratio of their decay rates.) 1911 Arthur Holmes publishes several uranium/lead ages based mostly on measurements taken by Boltwood and an improved value for the uranium decay rate. These range from 340 million years (a Carboniferous sample), to 1,640 million years (a Precambrian sample).
Even though Holmes' ages are incorrect, they eventually prove to be much better estimates than the best ones previously available to geologists (which were based on non-uniform and unreliable processes such as rates of sedimentation). Holmes' ages for Phanerozoic (Cambrian or later) samples are within 20% of the values given by modern methods. In the early 1900s, however, Holmes' results appeared to be at odds with other methods in common use, and they were not met with immediate acceptance from all quarters.
1913 J.J. Thompson observes that neon atoms have two different atomic weights (20 and 22), using equipment he calls a "positive-ray" apparatus. The existence of isotopes is confirmed. Unfortunately, it would take a long time to accumulate significant knowledge on the isotopes relevant to geological dating. Chemical dating methods won't entirely give way to isotope dating methods until almost 1940. 1917 J. Barrell publishes a Phanerozoic time scale based on chemical ages produced by Holmes (1911), and interpolations involving less quantitative methods. The divisions in the time scale fall fairly close to today's accepted values. For example, Barrell placed the Cenozoic-Mesozoic (Cretaceous-Tertiary) boundary at 55-65 million years ago (today's value: 65 million years ago), and the base of the Cambrian at 360-540 million years ago (today's value: 570 million years ago). 1920 F.W. Aston improves upon Thompson's (1913) positive-ray apparatus, and invents what he calls a "mass spectrograph." Using this device, he discovers a third isotope of neon with atomic weight 21. Aston devotes the remainder of his life to improving the design and precision of his device, and over time discovers 212 of the 287 naturally occurring isotopes.
Calculating an age for the Earth introduces additional complexity: even if it is a given that accurate ages for rocks can be obtained, there is no guarantee that the age of any given rock would be the age of the Earth. It would be necessary to either find rocks which formed at the same time as the Earth, or else come up with dating techniques that could "look back" through more recent events to the Earth's formation.
1921 Henry Russell calculates a maximum chemical age of eight billion years for the Earth's crust, based on estimates of its total uranium and lead content. Using the age of the oldest known (at that time) Precambrian minerals as a minimum for the Earth's age, Russell said:Taking the mean of this and the upper limit found above from the ratio of uranium to lead, we obtain 4 x 109 years as a rough approximation to the age of the Earth's crust.
(Russell 1921, quoted in Dalrymple 1991)
1927 Arthur Holmes publishes a booklet on the age of the Earth, which becomes fairly popular. The booklet contains a revised version of Russell's calculation, based on different estimates of the total quantity of uranium and lead in the Earth's crust. Holmes suggests that the age of the Earth is between 1.6 and 3 billion years. Twenty years after the first serious attempts at radioactive-decay ages (Boltwood 1907), the total number of computed mineral ages is still small enough that Holmes can summarize them all in one short table.
1927b F.W. Aston makes the first measurements of the isotopic ratios of "common lead." At this time it was already known that lead found in association with uranium had a relatively low atomic weight, but it seemed that all other lead (known as "common lead") had the same atomic weight. (The lighter atomic weight of lead in association with uranium is due to enrichment in 206Pb from decay of 238U. 206Pb is lighter than the atomic weight of common lead, which is about 207.2.) 1937 Alfred Nier begins to make a series of careful measurements on the isotopic composition of common lead. He discovers that the isotopic ratios of common lead can vary significantly, even in cases where the atomic weight does not. The most common radiogenic lead isotopes -- 208Pb (from 232Th) and 206Pb (from 238U) -- have on average roughly the same atomic weight as "common lead." As long as both are added in approximately equal amounts, the isotopic composition (relative to 204Pb) would be changed but the atomic weight would not.
Nier concludes that the variations in isotopic composition of "common lead" are due to mixture in varying degrees between radiogenic lead and "primeval" lead (which existed in a fixed, but at this point in time unknown, isotopic ratio at the time of formation of the Earth).
1941 Alfred Nier obtains and measures some ancient Pb ores which have the lowest 207Pb/204Pb and 206Pb/204Pb ratios of any rocks found to date. (204Pb is not produced by radioactive decay, while all other stable isotopes of lead are. The lower the ratio of other lead isotopes to 204Pb, the less radiogenic lead is present.) Nier speculates that these represent approximately the "primeval" Pb isotope ratios. 1941b E. Gerling uses Nier's (1941) "primeval" lead isotope ratios to create lead isotopic growth curves, and uses these to estimate a minimum age for the Earth's crust of 3.2 billion years. In doing so, Gerling devises the basic technique which will eventually produce an accurate age for the Earth and solar system.
Unfortunately, Gerling's original calculations are incorrect primarily because Nier's ancient lead ore is not truly "primeval" in composition. Though Gerling's result is within 30% of the actual age of the Earth, it is merely a good measurement of the age of Nier's samples rather than the age of the planet itself.
1944 During World War II, intense research on the atomic bomb leads to fantastic improvements in equipment for identifying and analyzing isotopes. It becomes possible to detect minute quantities of specific isotopes, and to measure their abundance with high precision. 1946 Alfred Nier improves on the design of the mass spectrometer and his machine shop builds dozens of the devices. The widespread availability of this equipment allows a much larger number of researchers to enter into the study of isotope geology. By the early 1950s, universities all over the world have laboratories dedicated to performing isotopic age assessments. 1946b Arthur Holmes produces calculations based on Nier's (1941) data. Holmes was unaware of Gerling's (1941b) work and attempted a slightly different technique. Holmes' computations result in a wide range of values; when plotted on a histogram, an obvious peak in the measurements occurs at about 3.3 billion years (a figure similar to Gerling's).
Holmes' computation involves the assumption that lead on Earth had been separated once long ago and the individual units had been allowed to evolve along independent isotopic growth curves. Due to that assumption being incorrect, Holmes mis-interprets scatter around a single growth curve as a number of independent growth curves. His work on tracing the "independent" curves back to their mutual intersection does not yield meaningful results.
1946c F. Houtermans independently performs calculations that are similar to Holmes' (1946b) and flawed in essentially the same way. His work is noteworthy in that he is the first to emphasize that the data on different isotopic growth curves would be co-linear if they started at the same point, and for these lines he coins the term "isochrones" (now known as "isochrons").
The evaluation of lead isotopic growth curves (somewhat unfairly to Gerling, known as the Holmes-Houtermans Model) holds promise, for it can look back through recent events to a point of origin. However, the key -- and still missing -- data needed in order to use such a method would be the lead isotopic ratios at the time of the Earth's formation (i.e., that of "primeval" lead).
1953 Clair C. Patterson produces accurate "primeval" lead isotopic measurements from minerals of the Canyon Diablo meteorite which contain very little (less than ten parts per billion) uranium. Meteorites provide the final solution to the puzzle, for they both are "rocks which formed at the same time as the Earth," and provide the important data which allows lead isotope computations to look back to the formation of the Earth. There had previously been no way to directly assess the age of the Earth; once meteorites were involved, suddenly there were several independent means.
In a recent issue of the Caltech Alumni Magazine, Clair Patterson discussed the ideas that led up to the measurement:
[Harrison] Brown had worked out this concept that the lead in iron meteorites was the kind of lead that was in the solar system when it was first formed, and that it was preserved in iron meteorites without change from uranium decay, because there is no uranium in iron meteorites. [...]
There are two isotopes of uranium that decayed to two different isotopes of lead, and there's also thorium, which decays to another isotope of lead. So you have three different isotopes of lead. And the whole thing gets mixed up. You've got all these separate age equations for the different isotopes of uranium and different isotopes of lead that were formed. [...] If we only knew what the isotopic composition of primordial lead was in the Earth at the time it formed, we could take that number and stick it into this marvelous equation that the atomic physicists had worked out. And you could turn the crank and blip--out would come the age of the Earth.
1953b F.G. Houtermans uses Patterson's (1953) data and the lead isotopic ratios of young terrestrial sediments, to compute a rough age for the Earth of 4.5 ± 0.3 billion years. These represent the first publication of the right value by a valid calculation.
However, Houtermans' calculations are essentially isochrons based on two data points (one data point for iron meteorites, another for young terrestrial sediments). Without additional data to tie the Earth and meteorites to a common source, the computed values are not guaranteed to be meaningful.
1956 Clair C. Patterson publishes an isochron age for the solar system (and therefore the Earth) of 4.55 ± 0.07 billion years. The age computation is based on Pb isotope analysis of five meteorites. Patterson points out that data for young Earth sediments fall on the same isochron; this implies that the Earth shares a common origin with the dated meteorites. Though only a few meteorites had been dated at this point in time, and the individual meteorite ages that did exist were not very precise, they also agree with the isochron age. 1998 A lot of data has been collected since Patterson's (1953, 1956) and Houtermans' (1953b) works. Precision of instruments has improved. Many more meteorites have been sampled and dated. Moon rocks have been sampled and dated. Decay constants have been measured with more accuracy. New techniques have been devised, tested, and applied.
The arrival of this new data has two effects: (1) some new data can be used to improve the precision of the original computations; and (2) new independent measurements confirm the original ones. Purely by coincidence, all of the adjustments (for example, current values of decay constants) to Patterson's 1956 computation have canceled each other out. Today's best estimate of the age of meteorites (4.55 ± 0.02 billion years) is identical to Patterson's value except for the smaller error range. That value has been confirmed dozens of times over.
The best estimate of the age of the Earth today is the same as that for meteorites: 4.55 ± 0.02 billion years. In the event that one wishes to be extra cautious in reporting a value, using the very generous error range of 4.5 ± 0.1 billion years is almost certain to encompass future changes as well.
For further detail on this topic, I strongly recommend G. Brent Dalrymple's The Age of the Earth.