To answer the question, we need to understand what radioactivity and half life is. We will take Uranium in our example. If Uranium isotope is used for dating a rock it doesn't mean that we need to know the original amount of Uranium in the sample. Half life calculation is completely a statistical process and rely on mathematics of large numbers.

Radioactivity is a random process in which if we just take one atom there is 50% probability of it getting decayed any time in future. That time can be within next second or in next millions of year. There is no certainly. What is certain, however is that some random atom within the sample is delaying at any time. For Uranium-235, 704 million years is the half life and that means that over 704 million years 50% of the atom in the sample would have become Lead-207.

In order to calculate the half life of Uranium, we just need to know:

1. Total number of current uranium atoms in the sample that can be measured with a chemical analysis, and 2. Number of Uranium atoms decaying per minute that can be measured using a Geiger counter reading (this is a common radiation detector, few models available on Amazon).

From above now we know the half life, only additional information we need to determine the age of rock, is the amount of daughter atoms (in this case Lead-207) in sample that the radioactive material decays into. This also is determined through chemical analysis.

Dating doesn't have to be extremely accurate when you try to date a rock billions of years old. With the best radioactive dating available right now you can achieve accuracy of +/- 2 million years, but in the context of billion of years, its pretty good. Its dependent on the half life of the element used. Thumb rule is to use element with half life at least 6 times the age of rock, so that enough of radioactive material is left to perform the test.

The half-life of radioactive isotopes can be determined experimentally. For example, one could use an instrument to read the radioactivity of a sample of pure isotope at an initial time and then find the time when half of the original isotope remains. I also wouldn't be surprised if there is a way to titrate for radioactive isotopes.

Even if the half-life of an isotope is known, more information is required before the isotope can be used for radiometric dating - the amount of the isotope that is typically found in rock/bone/etc. at any time. Scientists can then test a sample and determine its age by the ratio of radioactive isotope to its product after decay. For instance, in carbon dating, we know that a certain percentage of carbons in living tissue are found as Carbon-14, which is radioactive. When an organism dies, Carbon-14 is no longer incorporated into its tissues, so there is a known percentage of Carbon-14 for all given times after death, based upon Carbon-14's half-life, which is used to give age (time since death).

The age of organic matter is determined by Carbon Dating while that of Rocks is determined by the Potassium -Argon Dating.

I n determining the age of rocks,what is considered is the Radioactive Potassium 40 .This potassium isotope's rate of decay is not affected by pressure or temperature.It is ejected during a volcanic reaction and has a half life of 1.248Ã—10/\9 during which it slowly convert to Argon 40 gas.The ratio of the the undecayed potassium 40 to the quantity of Argon gas remaining is what is used to determine how long that rock has existed.Potassium Argon dating is used to measure the age of rocks older than 100,000 years and cannot be used for shorter timespans.

Carbon Dating is used to determine the age of organic matter since it died.During its lifetime,organic matter absorbs Carbon 14 into its bodyThe Carbon 14 starts to decay slowly.The amount left in the organic matter is what determine the age of the organic matter.Carbon dating however is not considered to be very accurate as it has a large range.

Although it is impossible to predict the exact time a single radioactive atom will decay, it is possible to use statistics on a large number of atoms and both predict and measure the decay. Using the idea of a half-life works very well. The assumption is that the probability of decay depends on the half-life (a constant) leads one to an exponential decay curve which is verifiable.

Statistical analysis of events in which the variables can be properly controlled or estimated is a logical and useful method. It works in quantum mechanics and in other probabilistic applications, such as poker, craps, artificial intelligence, and so on. Obviously, if there is an uncontrolled or unknown area it may not apply. Relating the height of a skirt with the price of stocks is one of those areas.

In order to know where we are on this exponential decay curve, it has to be calibrated somehow. This was described by Genera62 (above) with the example of Uranium decay.

There are a couple of ways to figure out what the original amount of substance was.

If the products of the radioactive decay are measurable and not present in the original sample, one can state the the original amount of the decayed isotope is the present amount plus the amount of the product. That is what Doodle58 wrote.

In Carbon dating one has to know the concentration of carbon dioxide in the air which is incorporated into the living organic matter. Also the weather during that growing season is important in determining the amount of CO2 taken up that year. And it is important to know the fraction of Carbon that is Carbon-14 at that time. All this is hard to calculate, and Carbon 14 dating has to be carefully calibrated from samples whose age is known from other techniques (like counting tree rings in a very old tree). The calibration problems with Carbon-14 dating make its accuracy less compelling than other techniques.

It seems illogical that you can tell how long it took to result in the current amount, of anything, without knowing the original amount. Statistically, anything is possible. A problem with that is that tere is no cause-and-effect relationship the parameters (correlation) (e.g... Height of women skirts is an indicator of that stock market will rise).

Statistics is invoked to explain the unknown: Predictions of future outcomes bases on previous data. If this is a valid approach, then there would be a lot more winners of the lottery and stock market players. In regard to quantum mechanics, verification of predictions because the outcomes are consistent with the fabricated superstructure and contoured by mathematical logic. In essence, verification is no proof. It only shows the outcome is consistent with the mathematics that were used to contour the paradigm.

I want to know how the original amount of substance is detemined. If the current amount is 12 ggams did substance start with 34 grams or 67 grams?

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