The **Half life formula**, a measure of the radioactive element gives information about the time required for the disintegration of one-half of the radioactive nuclei presents initially in the sample. **Half life or half life period** of a radioactive element is defined as *the time required for the disintegration of one-half of the original amount of radioactive element.* It is denoted by t_{1/2}.

**Half-life** is a characteristic unit for the exponential decay equation and is constant across a quantity’s lifetime. The shorter the t_{1/2}, the greater the number of atoms decaying in unit time. It may vary from a fraction of a second to millions of years.

## How to calculate half life?

If t_{1/2} is the half-life period of a radioactive element, then at t_{1/2}

N = 1/2 N_{o} ………………(i)

Substituting this value into rate equation for radioactive disintegration (v), we get

This is the required half life equation for a radioactive element.

## Half life formula

As per the above-derived equation, the half-life formula for the radioactive element is

## Relation between t and t_{1/2}

## Significance of half-life period

An element’s half-life time provides information on its stability. In comparison to isotopes with shorter half-lives, those with longer half-lives are generally more stable. Some of the major significance of the half-life period are:

- The half life period is independent of the initial amount of radioactive substance,
- A radioactive substance’s concentration is decreased by half after each half-life, and as a result, its activity is lowered by half as well. It may be calculated that the activity reduces to (1/2)
^{n}when ‘n’ half-life periods have passed. The following relation gives the amount of substance remaining after ‘n’ half-life periods.

## Half life video

## FAQs

### half life of uranium

The half life of uranium 238 is about 4.5 **×**10^{9} years, while that of uranium 235 is 700 million years.

### half life symbol

half life symbol is t_{1/2}

### What is the half life of carbon 14?

the half life of carbon 14 is about 5700 ± 30 years.

### half life of uranium 238

The half life of uranium 238 is about 4.5 **×**10^{9} years.

### half life of uranium 235

The half life of uranium 238 is about 700 million years.

## References

- Atkins, P. (2010). Shriver & Atkins’ Inorganic Chemistry (5th or later Edition). Oxford University Press.
- Lee, J. D. (2008). Concise Inorganic Chemistry: Fifth Edition by J.D. Lee (Fifth edition). Oxford University Press.
- Arun Bahl, B. S. Bahl & G. D. Tuli,
*Essentials of Physical Chemistry*, S. Chand and Company Ltd., New Delhi, 2012.