CHEM - Uranium isotope relative abundance at diff times

[thiev]

1. Homework Statement

The relative abundance of uranium isotopes in today’s Earth crustal material is:
99.2745% 238U
0.7196% 235U
0.0055% 234U
What were the relative abundances when the Earth was formed 4.6x109 years ago?


2. Homework Equations

t = age = 1/lambda * ln(N/No)

N = No*e^lambda*t

3. The Attempt at a Solution

i don't know how to approch this...

 

[The Bob]

Hey,

I agree with LowlyPion in the other post that you need to know the half-lives and then I think it will be a matter of ratios.

Just post a question the once for the future. This is so people helping you are seeing what everyone is saying and not repeating work that has already been done. We only want to help.

The Bob

 

[Blueshift5]

I would approach this problem by first understanding the concept of radioactive decay and how it affects the relative abundance of isotopes over time. Uranium-238 has a half-life of 4.5 billion years, while uranium-235 has a half-life of 700 million years. This means that over time, the amount of uranium-238 will decrease while the amount of uranium-235 will increase.

Using the equations provided, we can calculate the relative abundances of the uranium isotopes at the time of Earth's formation. Since we know the age of the Earth (4.6 billion years), we can plug that into the equation t = age = 1/lambda * ln(N/No) and solve for the initial amount (No) of each isotope.

For uranium-238, we would use the equation N = No*e^lambda*t, where lambda is the decay constant for uranium-238 (0.693/4.5 billion years). This would give us an initial amount (No) of 99.999% for uranium-238.

Similarly, for uranium-235, we would use the equation N = No*e^lambda*t, where lambda is the decay constant for uranium-235 (0.693/700 million years). This would give us an initial amount (No) of 0.001% for uranium-235.

For uranium-234, we can assume that it was not present at the time of Earth's formation, since its half-life is only 245,500 years. Therefore, the initial amount (No) for uranium-234 would be 0%.

In conclusion, the relative abundances of uranium isotopes at the time of Earth's formation would have been approximately 99.999% for uranium-238, 0.001% for uranium-235, and 0% for uranium-234. This is due to the natural process of radioactive decay, which has been occurring since the formation of the Earth.