# Substance decrease by factor of 100? (radioactivity)

## Homework Statement

Radioactive iodine (131-I) has a half life of 8 days. How long does it take for iodine to be reduced by factor of 100?

N(t)=N(o)e-kt
k=ln100/t1/2

## The Attempt at a Solution

N(t)=N(o)e-kt

N(t)/N(o)=e-ln(100/8)t

Now I'm stuck. I would think to to take the ln of both sides, but there isn't any values given for N(t) or N(o). Also, the value of k I'm pretty sure is right...Any confirmation on this?

Thanks alot for your help :)

Redbelly98
Staff Emeritus
Homework Helper
k=ln100/t1/2
Not true, you should look up this relation and use the correct one.

Now I'm stuck. I would think to to take the ln of both sides, but there isn't any values given for N(t) or N(o).
The phrase "to be reduced by factor of 100" suggests a relation between N(t) and N(o). It has nothing to do with the value of k.

collinsmark
Homework Helper
Gold Member
Now I'm stuck. I would think to to take the ln of both sides, but there isn't any values given for N(t) or N(o).

No, but you know the ratio of N(t)/N0 right? "...reduced by factor of 100.." Also, the value of k I'm pretty sure is right...Any confirmation on this?

Sorry, something is not quite right for your k value. You know the half life is 8 days. In other words,

N(8 days)/N0 = 1/2 = e-k(8 days). Solve for k.

Ok I think I got it:

N(o)/100 = N(o)e-kt

1/100 = e-kt

ln(1/100) = e-kt

ln(1/100) = -[(ln2)/8](t)

53.1 days = t

collinsmark
Homework Helper
Gold Member
Ok I think I got it:

N(o)/100 = N(o)e-kt

1/100 = e-kt

ln(1/100) = e-kt

ln(1/100) = -[(ln2)/8](t)

53.1 days = t

I think you forgot to express taking the natural log of the right side of the equation above in red (but it seems that you did later in the next step). (Any time you do something to one side of an equation, you must do the same thing to the other side, at the same time.) Anyway, your final answer is about the same as what I got (slightly different at the 4th significant digit). Yes, I just forgot to put it in. Thanks for your help :)