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Half-life

Here you can learn something Half-life is and how to calculate it. You will also see why this parameter is so important and what it says.

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Half-life simply explained

The Half-life is a parameter of radioactive nuclear decay. Do you observe a radioactive Atomic nucleus, can with a specific probability predict when it will disintegrate but do not give the exact time of emission. In order to be able to make statements about the remaining core, you use periods in which you know the target state of the core. The Half-life states the period of time after which a quantity that decreases over time has reached half of its original value. Take a size exponentially over time, it always remains the same, no matter from which point in the process you measure.

This key figure tells you after what period of time a variable that decreases exponentially over time has reached half of its original value.

Law of decay

Imagine you have a radioactive preparation with you Atomic nuclei. These disintegrate and have a activity. Then results for the number of in the time interval disintegrating nuclei the relationship:

You shape that to

You integrate this equation.

You then reshape that one last time

With that you have that Law of decay and the factor as Decay constant Are defined.

The Law of decay tells you how a given amount radioactive nuclei disintegrate over time. This decay depends on the original number of nuclides whose Half-life and from the time already passed.
Note, however, that the Law of decay makes no statement about individual atomic nuclei. Since it is a statistical law, one can only look at a set of atoms and make statements about their decay.

Decay constant

The Decay constant gives you the fraction of the available atomic nuclei that decays per second. It is an important constant that is associated with almost every statement about a decay. It plays an important role in calculating the lifespan, Half-life and Decay width.

As an example, you can use the lifespan of uranium-235 to calculate. This one has one Decay constant of. The lifespan is calculated from its reciprocal value, i.e.:

You set the Decay constant one results from it

So uranium-235 has one lifespan of about 1.016 billion years!

Half-life formula

With the help of Law of decay can you the Half-life to calculate. You assume that after time only half of the substance is left. This results in

You copy that around.

You can do the same for the general determination of the times of decay. Instead of then you put and reshape. From this then follows

So after a Half-life half of the atoms decay. After two there are still a quarter and after three an eighth of the original atoms are left.

Since you can derive the Law of decay do, this is also a statistical analysis. After a Half-life do you know that half of the atoms have decayed. However, you do not know what happened to the individual atoms.

Calculate half-life

A simple example will help you visualize the calculation. In the case of uranium-235, you have one Decay constant. Inserted into the equation results in Half-life uranium

So uranium-235 has one Half-life from 704 million Years!

As another example, consider carbon-14. This one has one Decay constant of .

To calculate the years you have to go through the value calculated in seconds share.

Half-life examples

The concept of Half-life can be used for any quantity that decreases exponentially over time. In this context, it is therefore also used in other areas. However, this parameter does not give you any information about individual parts in a system. It is a statistical representation of the events in a decreasing amount over time. Other methods are required to consider individual components.
In the following you will see other areas in which this term is used.

Radioactive half-life

The radioactive Half-life describes the period in which the amount of a radioactiveAtom, due to its decay, decreases by half. Also the activity of such an atom is reduced by half in this period of time.

Biological half-life

The biological Half-life, also Elimination half-life, describes the period in which the amount of an incorporated substance in an organism has fallen to half of its original value through all biological processes.

Effective half-life

The effective one Half-life describes the period in which the amount of a radioactiveAtomwhich has been incorporated in an organism has decreased by half. Here are the biological and the radioactive Half-life involved. Both effects can be used together in one Exponential function be summarized.

Bibliometric half-life

The bibliometric Half-life considers the decrease in citations of scientific publications over time. It has been found that citation, as well as the frequency of ordering copies of magazine articles, has halved after about five years.

Radiocarbon method

With the Radiocarbon method, carbon-containing, especially organic, substances are dated radiometrically. In dead organisms the amount of radioactive increases Atoms, according to the Law of decay from. By observing them, the age of a person can be determined within a range of 300 to 60,000 years.
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Further examples

Here are a few more important ones Half-lives.

carbon5,730 years
plutonium24,110 years
Thorium14.05 billion years
radon3.8 days
Cesium30.2 years