# Half life Formula- Definition, and Well-derived equation

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 t1/2.

Half-life is a characteristic unit for the exponential decay equation and is constant across a quantity’s lifetime. The shorter the t1/2, 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 t1/2 is the half-life period of a radioactive element, then at t1/2

N = 1/2 No ………………(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

## 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.

## FAQs

### half life of uranium

The half life of uranium 238 is about 4.5 ×109 years, while that of uranium 235 is 700 million years.

### half life symbol

half life symbol is t1/2

### 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 ×109 years.

### half life of uranium 235

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

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