Posted by **Bean** on Wednesday, February 28, 2007 at 6:09pm.

The isotope caesium 137 has a half life of 30 years. How long will it take for the amount of this isotope in a sample of caesium to decay to one sixteenth of its original amount? Please can someone explain how I can calculate this from the quantities that have been stated? Thanks

It decays 1/2 each 30 years.

time amount left

30 1/2

60 1/4

90 1/8

see the pattern?

Mathematically, it can be written as

amountleft/originalamount= (1/2)^{time/halflifetime}

or in logs

amount left/originalamount=e^{0.692time/halflifetime}

Saved by Bob again! Thank you!