Half Life Period

JEE Crash Course 2022

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 which 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) = No (½) t / t ½ 

N(t) = No 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

FAQs (Frequently Asked Questions)

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. What is the Shortest Half-Life?


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= -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.