Why are activities of all isotopes in a decay-chain equal?

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In summary, the activity of U-238 and U-234 in a uranium series must be equal because the decay constant only depends on the shape of the nucleus potential well and the number of atoms of each isotope affects their individual activities. As the number of U-238 atoms decreases, its activity decreases faster than U-234 until they reach the same activity.
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Clara Chung
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For example the activity of U-238 and U-234 in an uranium series is the same. Isn't activity depends on decay constant and the amount of atoms? Why must the activities equal and what is the reason behind?
 
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The decay constant only depends on the shape of the nucleus potential well.
 
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refer to question 32 and the solution of 32 thanks for help
 
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On a cell phone, can't read it.
 
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Clara Chung said:
For example the activity of U-238 and U-234 in an uranium series is the same. Isn't activity depends on decay constant and the amount of atoms? Why must the activities equal and what is the reason behind?
Consider a sample of radioactive material that contains a mixture of U-238 and U-234. Suppose that at some time the activity of the U-238 in the sample is greater than the activity of the U-234. How is the number of atoms of U-238 changing relative to the number of number of atoms of U-234, and how does that change affect the activity of each isotope?
 
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Nugatory said:
Consider a sample of radioactive material that contains a mixture of U-238 and U-234. Suppose that at some time the activity of the U-238 in the sample is greater than the activity of the U-234. How is the number of atoms of U-238 changing relative to the number of number of atoms of U-234, and how does that change affect the activity of each isotope?

thank you so much. Number atoms of 238 will decrease and while the number of 234 decreases in a slower rate because of lower activity and supply from 238. The activity of 238 decreases faster than 234 until they reaches the same activity.
 

1. Why are activities of all isotopes in a decay-chain equal?

The activities of isotopes in a decay-chain are equal because each isotope in the chain undergoes radioactive decay at a constant rate. This means that the number of atoms that decay per unit of time is the same for each isotope. As a result, the activities of all isotopes in the decay-chain are equal.

2. How does radioactive decay occur?

Radioactive decay occurs when the nucleus of an atom is unstable and releases energy in the form of radiation to become more stable. This can happen through different types of decay, such as alpha, beta, and gamma decay, which result in the formation of different isotopes.

3. What factors affect the rate of radioactive decay?

The rate of radioactive decay is primarily affected by the type of isotope and its half-life, which is the time it takes for half of the atoms in a sample to decay. Other factors that can influence the rate of decay include temperature, pressure, and the presence of external radiation.

4. Are there any exceptions to the equal activities of isotopes in a decay-chain?

In some cases, there can be slight variations in the activities of isotopes in a decay-chain due to the concept of secular equilibrium. This occurs when the half-life of an isotope is much longer than its parent isotope, leading to a buildup of the parent isotope in the decay-chain and a slight difference in activities.

5. Why is it important to understand the equal activities of isotopes in a decay-chain?

Understanding the equal activities of isotopes in a decay-chain is crucial in various fields, including nuclear medicine, environmental science, and geology. It allows us to accurately predict the behavior of radioactive materials and their impact on living organisms and the environment. This knowledge also plays a critical role in the safe handling and disposal of radioactive waste.

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