If Isotope A decays by 50% and Isotope B grows up to 50%, which one is the Daughter Isotope?

Question

If Isotope A decays by 50% and Isotope B grows up to 50%, which one is the Daughter Isotope?

BlackTom AI · Accepted Answer

A daughter isotope is the nuclide produced by the decay of a parent nuclide; therefore the isotope that increases in abundance as a result of the decay process is the daughter.

1. Relevant knowledge points and concepts
- Parent (or parent isotope): the original radioactive nuclide that undergoes decay and decreases in number over time.
- Daughter (or daughter isotope): the product nuclide formed by the decay of the parent; its abundance typically increases as the parent decays.
- Conservation of disintegrations: atoms lost from the parent appear as atoms of the daughter (ignoring other branches or subsequent decay).

2. Complete step-by-step reasoning
- The problem states Isotope A “decays by 50%” and Isotope B “grows up to 50%.”
- Decay of A means A is losing nuclei; growth of B means B is gaining nuclei.
- If the decay of A produces B, then B will increase by roughly the amount A decreases (subject to decay rates and branching). The qualitative clue “decays” vs “grows” identifies parent vs daughter.

3. Calculations and intermediate steps (numerical example)
- Assume initial amounts: A0 = 100 atoms, B0 = 100 atoms.
- A decays by 50% → A_final = 100 × (1 − 0.50) = 50 atoms; atoms lost = 50.
- B grows by 50% → B_final = 100 × (1 + 0.50) = 150 atoms; atoms gained = 50.
- The 50 atoms lost from A correspond to the 50 atoms gained by B, consistent with A → B decay producing B as the daughter.

4. Why the correct answer is correct
- The daughter isotope is the one whose abundance increases as a product of the parent’s decay. Since B’s abundance grows while A’s decreases, B must be the daughter.

5. Why the other option is incorrect
- Isotope A is decreasing (decaying), which identifies it as the parent, not the daughter. Therefore “Isotope A” cannot be the daughter.

6. Conclusion
Isotope B is the daughter isotope. This matches the provided correct answer: Isotope B.

If Isotope A decays by 50% and Isotope B grows up to 50%, which one is the Daughter Isotope? 多项选择题

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