# Homework Help: Half life

1. Aug 10, 2007

### mike2007

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

2. Aug 10, 2007

### Dick

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

3. Aug 10, 2007

### mgb_phys

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

4. Aug 10, 2007

### mike2007

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

5. Aug 10, 2007

### mike2007

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?????

6. Aug 10, 2007

### Dick

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.

7. Aug 10, 2007

### Dick

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.

8. Aug 10, 2007

### mike2007

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