How do you find radioactive decay half life?

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How do you find radioactive decay half life?

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Answer 1 · 2018-01-04T01:54:41

Use the radioactive decay half-life formula.

Explanation:

The radioactive decay half-life formula states that

$N (t) = N_{0} {(\frac{1}{2})}^{\frac{t}{t_{\frac{1}{2}}}}$ $N(t)=N_0(1/2)^(t/t_(1/2))$

where

$N (t)$ $N(t)$ is the final amount of substance

$N_{0}$ $N_0$ is the initial amount of a substance

$t$ $t$ is the time (usually in years or seconds)

$t_{\frac{1}{2}}$ $t_(1/2)$ is the half-life of the substance

To solve for half-life of a substance, rearrange the formula in terms of $t_{\frac{1}{2}}$ $t_(1/2)$ .

$N (t) = N_{0} {(\frac{1}{2})}^{\frac{t}{t_{\frac{1}{2}}}}$ $N(t)=N_0(1/2)^(t/t_(1/2))$
$\frac{N (t)}{N_{0}} = {(\frac{1}{2})}^{\frac{t}{t_{\frac{1}{2}}}}$ $(N(t))/N_0=(1/2)^(t/t_(1/2))$
${log}_{\frac{1}{2}} [\frac{N (t)}{N_{0}}] = \frac{t}{t_{\frac{1}{2}}}$ $log_(1/2)[(N(t))/N_0]=t/t_(1/2)$

$:.t_(1/2)=t/log_(1/2)[(N(t))/N_0]$

Source:
https://www.wikihow.com/Calculate-Half-Life

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How do you find radioactive decay half life?

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