# Exponential decay?

• May 7th 2009, 09:13 PM
tuzzzan
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.
• May 7th 2009, 10:29 PM
CaptainBlack
Quote:

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 $t_{1/2}$ is the half life we have:

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

so:

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

Take logs:

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

etc.

CB
• May 7th 2009, 10:58 PM
Ronson
Ahhhh thank you so very much, I understand now
Cheers