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# Half Life Decay Formula

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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## Radioactive Decay Formula Half Life

The time required to disintegrate half of the original amount of a substance is known as the decay half life of that radioactive substance. Decay half-life is constant over the whole life of the decay. The converse of decay half life is called doubling time.

According to the law of radioactivity, we know that
$\frac{N}{N_{0}}=\left(\frac{1}{2} \right )^{\frac{t}{T_{\frac{1}{2}}}}$

N=N_{0}e^{-\lambda t}

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

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