How can half-life be described in terms of radioactive decay?

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How can half-life be described in terms of radioactive decay?

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Answer 1 · 2015-09-05T21:22:59

It is the time taken for the intensity of the radioactive emission to decay to half of its original intensity.

Explanation:

This is by definition.
Most radioactive decay follows the natural logarithmic law, ie

$I (t) = I_{0} e^{- λ t}$ $I(t)=I_0e^(-lamdat$

Lamda is a constant which differs for different radioactive materials and that is why each on has a different half life.
So the half life is the time taken for I to reach exactly half of $I_{0}$ $I_0$ , ie

$t = t_{\frac{1}{2}} \Leftrightarrow I = \frac{1}{2} I_{0}$ $t=t_(1/2)iffI=1/2I_0$

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How can half-life be described in terms of radioactive decay?

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