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By Age of the Earth is understood the total time since the earth has existed in its present physical state as a planet. In Geology, this problem has always been found as one of the most complicated and controversial topics. Many conclusions were suggested on different lines but were rejected by equally strong objections.

It was only with the discovery of radioactivity that a new method giving an approximate age, with comparatively less chances of error were found. Presently, by any discussion on the problem of age of the Earth is understood a discussion of radioactive methods alone since all the other methods are highly speculative and already stand discarded. They are mentioned below only to show the curiosity among the scientists about the topic.

At present, the maximum age of the Earth as determined from radioactive dating is put at 4.6 × 10^{9} years, i.e., four point six billion years.

**Old Method Used for Determining the Age of the Earth: **

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Many thinkers have attempted to tackle the question of Age of Earth, though unsuccessfully, even in earlier periods. Thus, in Hindu mythology, the total age of the Earth is mentioned as 4.32 thousand million years, of which nearly one half (about two thousand million years) is believed to have been over by now.

Another religious view mentioned in geological literature just to show the trend of thinking on the problem is due to an Archbishop, Ussher. He calculated, from his interpretation of the Old Testament, a day in 4004 B.C. as the Day of Creation of the World. John Lightfoot even calculated the exact time and date: 8 p.m., FRIDAY, October 22, 4004 B.C.

The first scientific effort was, perhaps, due to George L.L.de Buffon, who believed, on the basis of cooling of the Earth from an originally hot mass, that the Earth could not have been older than 70,000 years.

More rational assessments were made in the 19^{th} century, of which those based on the rate of sedimentation and rate of accumulation of sodium in oceans dominated the scientific world for a good time. The first method involved the calculation of total thickness of the sedimentary formations of different geological times.

As the present rate of sedimentation is broadly known, this was made basis for calculating the time required for depositing the total thickness of the sedimentary rocks. It was estimated by Sollas that since the beginning of Huronian time (a geological stage indicating the beginning of geological time). 2,65,000 feet of strata had accumulated.

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By taking the rate of accumulation as 1 Foot/100 years, he arrived at a figure of 26.5 million years as the age of the oldest rocks of the Earth. In another method proposed by Jolly, it was the total concentration of sodium in waters of oceans that was considered. An age of 90 million years was calculated on that basis.

The above methods have inherent shortcomings. The rate of accumulation of sediments could never have been uniform; moreover, determination of total thickness of sedimentary strata accumulated since the beginning of the earth could never be correct and the sedimentary rocks are not the oldest rocks. Similar objections were raised against the sodium concentration method. Hence, with the discovery of radioactive decay of elements, these methods have been totally discarded and are mentioned only as of historical interest.

**New Methods Used for Determining the Age of the Earth: **

**Radioactivity: **

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In the 20^{th} century, the problem of the age of the Earth has been dealt with considerable success by methods based on radioactivity. It was French physicist Becquerel who discovered in 1895 that nuclei of certain elements are inherently unstable and are actually in a process of spontaneous disintegration at a constant race to form stable end products.

Subsequent studies by numerous scientists, chief among whom were Marie Curie, Pierre Curie and Rutherford, put radioactivity on firm foundations as a subject of great practical importance in numerous fields. In geology, numerous workers applied this science for determining the age of the Earth for a period of over 30 years (from 1905 to 1939) and obtained valuable data.

**Principles: **

The radioactive methods for the determination of age of the Earth are based on a simple application of theory of radioactivity. Supposing a rock sample obtained from any part of the crust of the earth contains a radioactive element A, that has been spontaneously decaying at a fixed rate to the end product element B. Obviously, it will also be containing some amount of the end product B. The change is akin to a chemical reaction of first order and can be represented by the relationship-

A → B

Evidently, if relative amounts (in terms of atoms) of elements A and B present in the sample are precisely known and the rate of radioactive decay of A to B is also known, then the time that has elapsed since the formation of the radioactive substance (and hence the age of the rock containing that element) can be calculated.

**i. Disintegration Constant (λ****): **

Rutherford framed a simple law on rate of radioactive disintegration which states that- **“A certain constant fraction of any sample of radioactive element undergoes change in a unit time.”**

In radioactive determination of age of the earth, the concept of disintegration constant (also called decay constant) is of fundamental importance.

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**It is derived as follows from a system A → B: **

(i) Let the original number of atoms in A (at the time of start of decay) = N_{o}

(ii) Let the time that has elapsed since the beginning of decay = t

(iii) Let the number of atoms present after interval t = N,

Then the rate of change,

dN/dt = λ N or λ dt = dN/N

where λ is the disintegration constant.

if t = 1 then λ = dN/N

From the above relationship, λ may be defined as the fraction of total number of atoms of the radioactive substance A at any time which disintegrates per second. Obviously, λ is a constant only for a particular radioactive element. It is independent of the original amount of the substance. Further, any physical or chemical changes occurring on the rock containing the radioactive element have no effect on this disintegration constant.

The rock containing both element A and the end product B (the parent and daughter of radioactive pair), their amounts being known precisely, will have a minimum age given by T as per following relationship –

where T is generally given in millions of years.

**ii. Half-Life: **

It has been observed that the rate of disintegration of radioactive elements shows considerable variation from element to element. In some elements it is so fast that they decay completely in a matter of minutes and seconds; whereas in others the radioactive decay takes place in inconceivably slow rates. It may take millions of years for a constant fraction of a radioactive element to decay to a stable end product.

It has been, therefore, found convenient to express the time required for decay of one-half fraction of the original substance as a standard unit. This time is termed as half-life period and has a constant value for each radioactive element. It may range from a few seconds to many million years in different radioactive elements. It is expressed as T_{1/2}. Table 2.1 gives half-life periods of a few well-studied radioactive elements.

The concept of half-life may be explained with the help of a simple graphical representation depicting decay of 1 g of a radioactive element, with half-life (T_{1/2}) of 10 years. After 10 years, one-half of its quantity or 0.5 g would have been decayed to a stable end product. Now the remaining 0.5 g forms the starting mass for decay. During the next half-life only half of this mass i.e. 0.5 × 1/2 = 0.250 g would decay.

Similarly at the beginning of the third half-life, 0.250 × 1/2 = 0.125 g would decay leaving behind 0.0625 g as the original mass for decay according to the same pattern. Hence, half-life of 10 years (or any value for that matter) does not signify that the total mass of any radioactive element will completely decay in twice the period of half-life.

**Methods: **

A number of methods based on radioactive decay have been used to determine the absolute age of the Earth. Of these, methods based on Uranium-Lead, Thorium-Lead, Rubidium-Strontium and Potassium-Argon involve the determination of exact amounts of the parent-daughter elements of the system. Methods based on ratios of different isotopes of lead found in the same sample have also been used to give better results.

**i. Uranium-Lead Method: **

Uranium is the heaviest element occurring in nature in two isotopes-** **U^{238} and U^{235}. Both of these isotopes are radioactive that produce stable isotopes of Lead^{206} and Lead^{207}. The end product Lead of either type is designated as radiogenic lead to differentiate it from common-non-radioactive pure lead.

**The decay of Uranium Isotopes takes place according to the following relationship: **

(i) U^{238 }—————- 8He^{1} + Pb^{206} (Half-life = 4.50 × 10^{9} years)

(ii) U^{235}—————- 7He^{4} + Lead^{207} (Half-life = 0.71 × 10^{9} years)

**Thorium also disintegrates into another lead isotope Pb ^{208} according to following relationship: **

(iii) Th^{232 }———- 6He^{4} + Pb^{208} (Half-life = 1.39 × 10^{10} years)

In rock age determination using Uranium, the procedure involves spectrometric analysis of the specimen to determine the exact amounts of uranium isotopes and lead isotopes.

**Age of the specimen is then calculated by the relationship: **

Pb^{206} = U^{238} (e^{}^{8T} – 1)

Where Pb and U specify the amounts of isotopes; λ_{8} is the constant depending upon characteristics of U^{238} and T is the Age in years.

Uranium-lead isotopes analyzed from different parts have given the maximum age of the samples as 3.6 × 10^{9} years. This simply means that the Earth cannot be younger than 3.6 billion years. The mineral Pitchblende is the source for such isotopes.

**ii. Rubidium-Strontium Method: **

Rubidium^{87} undergoes radioactive transformation to Strontium^{87} by emitting β rays with a very large half-life (T_{1/2}) of 4.7 × 10^{10} years. This provides a very reliable method in determining age of some of easily available oldest rocks. The source minerals are different varieties of mica such as Iepidolite and muscovite. Methods consist of determining total rubidium and strontium content of the sample by latest isotope dilution techniques.

**The Age formula for Rb-Sr is as follows: **

where T = age of the specimen in million years; Sr and Rb indicate number of radiogenic atoms of the respective elements. This method has yielded ages of 2700 million years for the specimens studied.

**iii. Lead-Lead Method: **

It is known that different isotopes of radiogenic lead may be produced in the same sample by decay of different isotopes of Uranium, e.g. U^{235} → Pb^{207} and U^{238} → pb^{206}. The ratio of radioactive lead isotopes Pb^{207}/Pb^{206} formed during the decay of uranium in itself offers an easy method for finding out the age of the sample. It is easy because the job involves measuring only the ratio of lead isotopes.

**Age of the sample is determined using the relationship: **

where T is age of the specimen.

**iv. Meteoric Lead Method: **

It is considered as the most reliable method for determining age of the earth. It is based on isolation of Lead from iron and stone meteorites. Their isotopic compositions are determined and compared. The age of the Earth calculated from these ratios is around 4.6 × 10^{9} years. This is based on the assumption that the meteorites are also planet-like small bodies that have been formed in the solar system at the same time as our Earth.

**Conclusion: **

Radiometric age determination gives broader limits about the age of the Earth. The age determination on the granites of Greenland and from many other continents is around 3.8 billion years. Hence the Earth cannot be younger to those rocks formed on it. This is the lower limit.

Age determination on numerous samples of meteorites that are almost conclusively believed to have formed at the same time from the same type of source material as the Earth provides data indicating upper limits around 4.55 billion years.

Moon is believed to be as much a part of solar system as the Earth. Radiometric dating of lunar rock samples have also indicated age of 4.61 billion years.

Hence, as a matter of safe estimates, we may make an inference of age of the Earth at 4.6 billion years.