In 1896, the famous scientist Antonie Henri Becquerel was introduced the decay half life formula. According to him, the decay half life is the time period required for a substance to decay half of the original amount. This measurement is very much useful to determine the characteristics of an unstable atom. This decay is known as radioactive decay.

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According to the law of radioactivity, we know that

$\frac{N}{N_{0}}=\left(\frac{1}{2} \right )^{\frac{t}{T_{\frac{1}{2}}}}$

When we consider the half life, t = T _{1/2} (half life), then N = ^{N0}/ _{2}

Taking logarithm on both the sides we get,

$T_{\frac{1}{2}}$=$\frac{0.6931}{\lambda }$

Where

**$T_{\frac{1}{2}}$** is the half life period

**$\lambda$** is the decay constant

Characteristics of Half life formula

- Since we know that the decay half life time of the radioactive substance is inversely proportional to the rate of disintegration, so , if the rate of disintegration constant is more means half life will be small. If the decay half-life is small the radioactive substance will decay rapidly.
- In the decay half life formula the decay half life is not affected by the change in temperature and the change in pressure.
- In the decay half life formula the decay half life is different for different radioactive substances.
- According to the decay half life formula, the decay constant can be determined by using the value of half life.
- The number of undecayed atoms in the radioactive substance after n half lives is given by. $\frac{N}{N_{0}}=\left(\frac{1}{2} \right )^{\frac{t}{T_{\frac{1}{2}}}}$