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

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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
 
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.