# Uranium Dating

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1. Jan 4, 2015

### Purple Baron

1. The problem statement, all variables and given/known data
The isostopc abundances of a sample is U-235 and U-238 are 0.72 and 99.27 respectively; what is the age of the sample? (assume isotope abundance was equal when sample was formed)

2. Relevant equations
$\lambda=\frac{ln2}{ t_{\frac{1}{2}}}$

3. The attempt at a solution
for U-238 $N_{238}(T)=N_{238}(t)e^{\lambda _{238}t}$
U-235 $N_{235}(T)=N_{235}(t)e^{\lambda _{235}t}$
T is time at present and t is time of sample formation.

diving the two equations gives
$\frac{N_{238}(T)}{N_{235}(T)}=\frac{N_{238}(t)}{N_{235}(t)}e^{(\lambda _{238}- \lambda _{235})t}$

From the assumption, one can say $\frac{N_{238}(t)}{N_{235}(t)}=1$
It's here where i'm not sure; do i just say that $\frac{N_{238}(T)}{N_{235}(T)}=\frac{99.27}{0.72}$ and solve for t or am I missing something? Thanks

EDIT: Sorry, I can't get my latex to work, I can't seem to fix it

Last edited: Jan 4, 2015
2. Jan 4, 2015

### Staff: Mentor

I fixed the two broken equations, but the first one looks odd.
Yes, just do that and solve for t.

3. Jan 4, 2015

### Purple Baron

Thanks for that, I fixed the first equation.