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teddybear365 · Apr 29, 2009, 02:52 PM

1. Choosing an isotope where the half life is given in days calculate what percentage of a sample would remain after 5 days.
2. For an isotope where the half life is in years how much would be left after 100 years?
3. For an isotope where the half life is in hours, how much would be left after 48 hours?

Ra-224 halflife =3.6319 days
U-240 halflife = 14.1 hours
Cf-252 half life = 2.645 years

Equation = Nt = N0e − λt

galactus · Apr 30, 2009, 08:39 AM

Please use proper grouping symbols. I think your equation is meant to be:

$N(t)=N(0)e^{-kt}$

I used k instead of lambda.

k, the constant of proportionality, can be found from the formula

$T=-\frac{1}{k}ln(2)$

T is given as 3.6319 days, so solve for k.

Because it is a percentage remaining, you could let N(0), the amount initially, to be 1 for 100%. Then, using $e^{-kt}$ , where t=5, you can find the amount remaining at 5 days.

Do the other ones similarly. Just make sure your units are consistent.