Radium-226 has a half life of 1620 years. Find the time period during which a given mass of this material is reduced by one-quarter.

Q= Ce^-rt should be the right equation?

Stumped on how to set this up.

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- Feb 21st 2011, 10:40 PMdmbocciRadioactive decay
Radium-226 has a half life of 1620 years. Find the time period during which a given mass of this material is reduced by one-quarter.

Q= Ce^-rt should be the right equation?

Stumped on how to set this up. - Feb 21st 2011, 11:45 PMCaptainBlack
Because you are given a half life it is better to work with powers of $\displaystyle $$2$ rather than $\displaystyle $$e$. So:

$\displaystyle Q(t)=Q(0)\times 2^{-t/\tau}$

where $\displaystyle $$\tau$ is the half life.

Now if at time $\displaystyle $$t;\ Q(t)=Q(0)/4$ we have:

$\displaystyle 2^{-t/\tau}=1/4$

CB