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Half Life Period

Last updated date: 13th Jul 2024
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The amount of time it takes to disintegrate by half an initial amount.


The time it took to turn half a reactant into the product(s). The time required to undergo radioactive decay in half of a given sample. Half-life definition: The time it takes for half the atoms of an unstable element or nuclide to decay radioactively into another element or nuclide


For a given reaction, a reactant's half-life t1/2 is the time it takes for its concentration to reach a value which is the arithmetic mean of its initial and final (equilibrium) value. For a fully consumed reactant, it is the time it takes for the concentration of the reactant to fall to half its initial value. For a first-order reaction, the reactant's half-life may be called the reaction's half-life. In nuclear chemistry, (radioactive) half-life is defined as the time required for the operation to decrease by that process to half its value, for a simple process of radioactive decay.


Half-Life Definition

Half-Life is usually defined as the time it takes for a radioactive substance (or one-half of the atoms) to disintegrate or turn into another. The theory was first explored by Ernest Rutherford in 1907. Typically the symbol Ug or t1/2 reflects this.


If we take a radioactive element that has a half-life of one hour to help you understand the concept better.


Ok, if the radioactive element is taken in a case where half of the atoms have decayed after half a lifetime, it would be appropriate to assume that they have a well-defined average viz life expectancy. Atoms with a mean life that is considerably longer than their half-life. This would mean the mean life would be the half-life divided by 2 which is the standard algorithm. The half-life, on the other hand, is often represented in probability terms.


Half-Life Formulas

Below you'll find the half-life formulas used to explain the deterioration of substances.


N(t) = \[\frac {(1/2) t} {t 1/2}\] 


N(t) = No \[\frac {e-t} {r}\]


N(t) = No e– λt


Consider the following,


N0 = the initial quantity of the substance


N(t) = the quantity that is left over


t1⁄2 = half-life


τ = mean lifetime of the decaying quantity


λ = decay constant


Probabilistic Nature of Half-Life

A half-life generally explains the deterioration of distinct elements, such as radioactive atoms. Within this scenario, it does not operate to use the definition. That implies half-life is the duration needed for precisely half of the components to decay". For instance, if there is only one radioactive atom, and its half-life is one second. Then there won’t be any half of an atom left after one second. Rather, the half-life is described in terms of probability. In other words, the likelihood of a radioactive atom decaying within its half-life is 50 percent. After one half-life there are not precisely one-half of the atoms remaining, just roughly, because of the random variance in the operation. However, when there are many similar atoms decaying, the law of big numbers shows that it is a fairly reasonable estimate to claim that half of the atoms exist after one half-life. Several basic tasks can show probabilistic decay, for example via flipping coins or running a statistical software code.


Half-Life in Non-Exponential Decay

The term "half-life" is nearly solely utilized for decay procedures that are exponential, or roughly exponential). In a decay mechanism that is not even close to exponential, the half-life will shift substantially. Whereas decay is occurring. In this situation, it is usually uncommon to talk about half-life in the first place. However, sometimes folks will characterize the decay in terms of its "first half-life", "second half-life", etc., where the first half-life is described as the moment required for deterioration from the initial value to 50 percent, the second half-life is from 50 percent to 25 percent, and so on.


Half Time

Half time is the period needed for a variable to attain one half of its extremal level, wherein the amount of change is proportional to the difference of the present value and the extremal value. It is identical with a half-life, although used in somewhat different situations. The graphic demonstrates the growth in the quantity in response to a step-change in the motive force that affects it. The time-axis is in quantities of the half time. It can be observed that the quantity grows to one-half of its ultimate value after one-half time, to three-quarters after two half times, to seven-eighths after three half times, and so on. 


If the amount diminishes in relation to a step-decrease in the motive force that alters it, the curve is reflected in the time-axis and may be described as exponential decay. The idea of half time is employed in diving physiology when human tissues take in and discharge inert gases, typically nitrogen with changes in depth. Varied tissue types have various half durations for a particular inert gas. Thus predicting the absorption and discharge of gases by the tissues is vital to prevent decompression sickness. 



Radioactivity, property displayed by some types of materials of producing energy and subatomic events naturally. It is, in effect, a characteristic of particular atomic nuclei. An insecure nucleus will dissolve spontaneously, or decay, into a relatively secure structure. However, this happens only in a few precise ways by releasing certain particles or certain kinds of electromagnetic radiation. Radioactive decay is a feature of numerous naturally occurring elements as well as of intentionally created isotopes of the elements. The rate is represented in terms of its half-life of any specified amount of the isotope to decay, at which a radioactive element decays. Half-lives range from more than 1024 years for certain nuclei to less than 10−23 seconds. The procedure repeats till a steady nuclide has been created.


The Nature of Radioactive Emissions

The emissions of the most prevalent kinds of uncontrolled radioactive decay are four. The alpha particle is really the core of a helium-4 atom, having two positive charges.  Such electrified atoms are termed ions. The neutralized helium atom has two ions beyond its nucleus which balances these two charges. Beta particles may be negatively charged, or positively charged. The beta minus [β−] atom is essentially an electron generated in the nucleus after beta decay without any tie to the orbital electron array of the atom. The beta plus particle, also called the positron, is the antiparticle of the electron; if put along, two such particles will mutually destroy each other. 

FAQs on Half Life Period

1. How do you calculate half-life?

Formulas for half-life in exponential decay

  • N0 is the initial quantity of the decaying material (this quantity can be measured in grams, moles, number of atoms, etc.),

  • N(t) is the quantity that remains after a time t and has not yet decayed.

  • The half - life of the decaying number is t1⁄2

2. How long is a radioactive half-life?

The term half-life is defined as the amount of time it takes to disintegrate half the atoms of radioactive material.

3.  Which object has the shortest half-life?

Francium -You may wonder which object has the shortest half-life of all-natural occurrences. This would be francium, element 87, whose longest-lived isotope, francium-223, has a half-life of 22 minutes, decaying through beta-decay or alpha-emission a statin into the radium.

4. Is the radioactive decay formula?

Average number of radioactive decays per unit time (rate) or Change in number of present radioactive nuclei: A= \[\frac {-dN} {dt}\]

Depends on the number of current nuclei (N). Over time, A will decrease during the decay of a given sample.

5. Define half-life?

The time required to undergo radioactive decay for half the nuclei of a given radionuclide or radioactive material. Half-life fitness. The time required to be metabolized or removed by usual biological processes for half the amount of a medication or other substance accumulated in a living organism.