[Macg73]

The isotope caesium -137, which has a half life of 30 years, is a product of nuclear power plants. How long will it take for the amount of this isotope in a sample to decay to one-sixteenth of its original amount? Struugling with my chemistry at the moment, any advice on how to get started on this question gratefully recieved.

[enahs]

Start with your equation for half-life:
t_1/2 = ln (2) / k
You know the half-life (t_1/2), ln(2) is just a constant, solve for K.

Now from there? This is a first order reaction, go back to your kinetics.

[Yggdrasil]

A simpler solution:

The half life of your isotope is 30 years.  After 30 years, how much of your original sample is left. After 60 years, how much of your original sample is left?  After 90 years, how much of your original sample is left?  Do you see a pattern?

[Macg73]

Thanks, just to double check would that mean it will take 4 half-life intervals to decay to that amount, that is 120 years?

[Borek]

Yep.

[enahs]

Bah, I read that as 1/6th, not 16th. Yes that method is much easier, but only valid for nice intervals actually occurring on a factor of the half life.