Nuclear u-235 and u-238 isotope half life question

In summary, the present day value of the uranium isotopic ratio U-235/U-238 is 0.00723 and the half-lives of U-235 and U-238 are 7.13 x 10^8 and 4.51 x 10^9 years, respectively. To find the U-235/U-238 isotopic ratio 2 billion years ago, we can use the equations for the activity of each isotope as a function of time and divide them. When we substitute t = 2 billion years, we get a ratio of 0.1947. However, this may not be the correct answer and further investigation is needed.
  • #1
debwaldy
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0

Homework Statement



The present day value of the uranium isotopic ratio U-235/U-238 is 0.00723. The half life of U-238 is 4.51 x 10^9 and the half life of U-235 is 7.13 x 10^8 years. What was the U-235/U-238 isotopic ratio 2 billion years ago when the Oklo natural reactor was active?

Homework Equations


T1/2 = ln (2) / λ
τ = 1/λ
N(t) = No e^(-kt)


The Attempt at a Solution




Calculated the decay constant lambda for each isotope:

U-235: λ = 9.72 x 10^-10 per year

U-238: λ = 1.54 x 10^-10 years,

I'm not sure how to proceed or what I need to do next

New to this radioactive decay stuff so any tips or suggestions would be much appreciated.

Thanks,
Debbie
 
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  • #2
You have 2 equations, one for the activity of U-235 and one for the activity of U-238, each as a function of time. What happens when you divide one by the other?
 
  • #3
As in the equation N(t) equations? will the No be different in each case?
 
  • #4
If i do this and substitute in t = 2 billion years i get a ratio of 0.1947, although I don't think that this is correct?
 
  • #5




Hello Debbie,

Thank you for your question. To solve this problem, we will use the equations you have listed in your attempt at a solution. We will also make use of the fact that the ratio of U-235 to U-238 isotopes is constant throughout the decay process. This means that the ratio of the initial amount of U-235 to U-238 is equal to the ratio of the present day amount of U-235 to U-238. We will use this concept to solve for the initial U-235/U-238 isotopic ratio 2 billion years ago when the Oklo natural reactor was active.

First, we need to find the initial amount of U-235 and U-238 isotopes. We can do this by rearranging the equation N(t) = No e^(-kt) to solve for No. This gives us No = N(t) / e^(-kt). We can then substitute in our known values for N(t) (present day value) and t (2 billion years) to find the initial amount of each isotope.

Next, we can use the equation T1/2 = ln (2) / λ to solve for the decay constant k. We will use the half-life values given in the homework statement to find the decay constants for U-235 and U-238.

Finally, we can use the ratio of the initial amounts of U-235 and U-238 to find the initial U-235/U-238 isotopic ratio. This will give us the answer to the homework question.

I hope this helps. Please let me know if you have any further questions or need clarification on any of the steps. Keep up the good work in your studies of radioactive decay!

Best,
 

1. What is the difference between U-235 and U-238 isotopes?

U-235 and U-238 are two different isotopes of uranium. The main difference between them is their atomic mass, with U-235 having 235 nucleons (protons and neutrons) and U-238 having 238 nucleons. They also have different levels of radioactivity and half-life.

2. What is the half-life of U-235 and U-238?

The half-life of an isotope refers to the amount of time it takes for half of the original sample to decay. The half-life of U-235 is about 703.8 million years, while the half-life of U-238 is much longer at about 4.47 billion years.

3. How is the half-life of an isotope determined?

The half-life of an isotope is determined by its rate of decay, which is constant for each isotope. This rate is measured by the number of radioactive particles emitted per second, which is known as the decay rate. By measuring the decay rate over time, the half-life can be calculated.

4. What is the significance of U-235's shorter half-life compared to U-238?

The shorter half-life of U-235 means that it is more unstable and decays at a faster rate than U-238. This makes it useful for nuclear reactions, as it can sustain a chain reaction and release a large amount of energy. On the other hand, U-238 has a longer half-life and is more commonly used as a source for nuclear fuel.

5. How is U-235 used in nuclear power and weapons?

U-235 is used in nuclear power plants as a fuel source, where it undergoes controlled fission reactions to produce heat, which is then used to generate electricity. It is also used in nuclear weapons, as the chain reaction created by its fission can result in a powerful explosion. However, the use of U-235 in nuclear weapons is heavily regulated and controlled due to its potential for mass destruction.

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