# Half life

If the rate of an isotope in 18 days has dropped by one eight of its initial value. what is the half life of the isotope?

In 18 days the rate has dropped by 1/8 so therefore the half life is 4/8 which is 18*4 = 72days

Dick
Homework Helper
That's wrong. What's the formula for the rate as a function of initial rate, elapsed time and half life?

mgb_phys
Homework Helper
Or even if you haven't studied the formula.
After one half-life what is the rate, after two, after three ....?

T1/2 = ln(2)/lambda
Thats the formula i think will work.

1/2*1/2*1/2 = 1/8
so there will be three half lives after 18 days. So therefore one half life is 6 days?????

Dick
Homework Helper
Here's a better one:

R(t)=R(0)*(2^(-t/th)). Where R(t) is the rate at time t, and th is the half life time.

Dick
Homework Helper
1/2*1/2*1/2 = 1/8
so there will be three half lives after 18 days. So therefore one half life is 6 days?????

Yes, if you mean the final rate is 1/8 of the initial rate. I thought by saying 'dropped by one eighth' you meant that the final rate was 7/8 of the initial rate.

Yes that is what it means, sorry about the mistake.
Thank you very much for the clarification.