# Homework Help: Uranium isotopes percentage 4.5 billion years ago

1. Dec 5, 2013

### HaiderAbbas

1. The problem statement, all variables and given/known data

Given T(1/2) of U-235 = 7.04x10^8 yrs (0.7%)
T(1/2) 0f U-238 = 4.468x10^9 yrs (99.3%)
Calculate percentage of U-235 & U-238 at the time of creation of earth(~4.5 billion years ago)

2. Relevant equations

N(t) = No e^(-λt)

3. The attempt at a solution
λ(U-235) = 9.84x10^-10 per year

λ(U-238) = 1.55x10^-10

Now m confused how to proceed further with percentages...???

2. Dec 5, 2013

### ehild

Today 0.7% of the whole amount of the Uranium mineral is a rock is U235, and 99.3 % is U238. If you call N1(t) the amount of U235 and N2(t) the amount of U238 at time t, then

N1(t)=N1(0) e^(-λ1t)

and

N2(t)=N2(0) e^(-λ2t),

where N1(0) and N2(0) are the amounts of U235 and U238 at the time when the Earth was created. (We assume that mineral have been intact since then.)
You know that

N1(t)/(N1(t)+N2(t)) =0.007

and

N2(t)/(N1(t)+N2(t))=0.993.

Determine the ratio N1(0)/(N1(0)+N2(0)).

ehild