1. ## Exponential decay?

Hi i've been stuck on a question for ages and don't know if i have even got it right or not, anyone able to help?

A radioactive mass M(g) in a lump of material is given by M=20e^-0.0015t where t is the time in seconds since the first observation

i) what is the initial size of the mass?

I have 20g down for this since t=0

ii) what is the mass after 1 hour?

i have 0.0903g since t=3600

iii) the half life of a radioactive substance is the time it takes to decay to half its mass. What is the half life of this material?

I can only get this by the trial and error approach and would like help if anyone can tell me how to work it out.

2. Originally Posted by tuzzzan
Hi i've been stuck on a question for ages and don't know if i have even got it right or not, anyone able to help?

A radioactive mass M(g) in a lump of material is given by M=20e^-0.0015t where t is the time in seconds since the first observation

i) what is the initial size of the mass?

I have 20g down for this since t=0

ii) what is the mass after 1 hour?

i have 0.0903g since t=3600

iii) the half life of a radioactive substance is the time it takes to decay to half its mass. What is the half life of this material?

I can only get this by the trial and error approach and would like help if anyone can tell me how to work it out.
If $\displaystyle t_{1/2}$ is the half life we have:

$\displaystyle 10=20 ~e^{-0.0015 t_{1/2}}$

so:

$\displaystyle e^{-0.0015 t_{1/2}}=0.5$

Take logs:

$\displaystyle -0.0015 t_{1/2}=\ln(0.5)$

etc.

CB

3. Ahhhh thank you so very much, I understand now
Cheers