• Oct 5th 2012, 11:50 PM
Filmstrip
Hey guys, just found this forum after searching for days about this problem I've got. No where seems to have any relevant answers so I thought I might ask a forum for some help.
Basically I've got a Methods Assignment and I can't seem to work out if what I am doing is correct, any help would be great.
Here's the question:
The mass of a radioactive isotope is given by M=Mo(10)^-kt. It takes 200 years for the mass of the isotope to halve.
Find the initial mass (grams) in terms of M.
I assume Mo10(10) is the initial mass and a logarithm, doesn't say though.

I've tried to solve this question like this:
M=Mo10(10)-kt
M=(-kt)Mo10(10)
M/Mo10(10)=-kt
Mo10(10)/M=1/-kt
Mo10(10)=-M/kt

Is this correct or have I made some kind of mistake, just doesn't seem right to me :/
• Oct 6th 2012, 12:01 AM
MarkFL
If it takes 200 years for half of the isotope to decay, then we may state:

$\displaystyle \frac{1}{2}m_0=m_0\cdot10^{-200k}$

$\displaystyle \frac{1}{2}=10^{-200k}$

$\displaystyle \log(2)=200k$

$\displaystyle k=\frac{1}{200}\log(2)$

$\displaystyle M=m_0\cdot10^{-\frac{t}{200}\log(2)}=m_0\cdot2^{-\frac{t}{200}}$

$\displaystyle m_0=M\cdot2^{\frac{t}{200}}$
• Oct 6th 2012, 12:34 AM
Filmstrip