The half life of a radioactive substance is 12 years. When will 90% of the material have dissipated?

Question

schrodingers_cat · Answer

Start with N(t) = No(1/2)^(t/t1/2)

t1/2 = half life

You want to know when you 90 % of No has dissipated.

So,

(.1)(No) = No(1/2)^(t/t1/2)

Divide by No and take the log of both sides,

log(.1) = (t/t1/2)log(1/2)

Solve for t,

t = (12)log(.1)/(log(1/2) = 39.86 years

Hope this helps :)

anonymous · Answer

@Schrodingers_Cat  thank you for aking your time to help me.. but how did you get .1 isn't supposed to be .9 since it is 90%?

schrodingers_cat · Answer

You want to know when 90% of the material has dissipated. So, only 10% will be left :)

anonymous · Answer

Oh okay thank you so much @Schrodingers_Cat

schrodingers_cat · Answer

No Problem :)

wolf1728 · Answer

We can use the formula: elapsed time = half life * log (beginning amount / ending amount) / log 2 elapsed time = 12 * log(100 / 10) / log(2) elapsed time = 12 * 1 / 0.3010299957 elapsed time = 39.8631371386 years You can find half life formulas and a calculator here: http://www.1728.org/halflife.htm