#HALF LIFE CHEMISTRY CALCULATOR CODE#

#HALF LIFE CHEMISTRY CALCULATOR CODE#

The code runs fine, however for this series I am getting a halflife of 680.5 days - I can see from the chart that this looks very wrong. #run OLS regression to find regression coefficient to use as 'theta' #set up lagged series of z_array and return series of z_array I am carrying out the following using python code to find the halflife (FYI the series shown above is held in the variable (z_array): import numpy as np Which obviously looks rather mean reverting. I have a series which when plotted looks like: There are various simple exercises that demonstrate probabilistic decay, for example involving flipping coins or running a statistical computer program.Īn exponential decay process can be described with respect to half-life as shown here.I am currently attempting to calculate the halflife of a mean reverting series using python programming language and the theory of the Ornstein–Uhlenbeck process. Nevertheless, when there are many identical atoms decaying (right boxes), the law of large numbers suggests that it is a very good approximation to say that half of the atoms remain after one half-life. Note that after one half-life there are not exactly one-half of the atoms remaining, only approximately, because of the random variation in the process. In other words, the probability of a radioactive atom decaying within its half-life is 50%.įor example, the image on the right is a simulation of many identical atoms undergoing radioactive decay.

Instead, the half-life is defined in terms of probability: “Half-life is the time required for exactly half of the entities to decay on average”. For example, if there are 3 radioactive atoms with a half-life of one second, there will not be “1.5 atoms” left after one second. In that case, it does not work to use the definition “half-life is the time required for exactly half of the entities to decay”. The converse of half-life is doubling time.Ī half-life usually describes the decay of discrete entities, such as radioactive atoms. For a general introduction and description of non-exponential decay, see rate law. For a general introduction and description of exponential decay, see exponential decay.

The table on the right shows the reduction of a quantity in the number of half-lives elapsed. The term “half-life” may generically be used to refer to any period of time in which a quantity falls by half, even if the decay is not exponential. It is a characteristic unit for the exponential decay equation. Half-life is used to describe a quantity undergoing exponential decay, and is constant over the lifetime of the decaying quantity. Rutherford applied the principle of a radioactive element’s half-life to studies of age determination of rocks by measuring the decay period of radium to lead-206. The original term, dating to Ernest Rutherford’s discovery of the principle in 1907, was “half-life period”, which was shortened to “half-life” in the early 1950s.

The term is very commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay, but it is also used more generally for discussing any type of exponential decay. Half-life is the amount of time required for the amount of something to fall to half its initial value.

Half life chemistry calculator