Answer :
Final answer:
To produce Francium-223 via three alpha and two beta decays, we identify that we must start from Astatine-210. Each decay type modifies the atomic and mass numbers, leading us ultimately to Francium. Astatine-210 is the correct parent isotope for this series of decays.
Explanation:
Decoding the Decays to Produce Francium-223
To produce Francium-223 through a series of radioactive decays, we start with a parent nucleus and track its transformations. The decay process involves three alpha (α) decays and two beta (β) decays. Each alpha decay reduces the atomic number by 2 and the mass number by 4, while each beta decay increases the atomic number by 1 without changing the mass number.
1. Starting Point
We need to determine which given element will yield Francium-223 ([223 Fr]). The atomic number of Francium is 87. To find the parent nuclide, perform the reverse calculations:
- Starting with Francium-223 (mass = 223, atomic number = 87).
- First, reverse two beta decays:
- Adding two (β) to the atomic number: 87 - 2 = 85.
- Now, we perform three alpha decays:
- For each α decay, reduce atomic number by 2 and mass by 4:
- 1st α decay: 85 + 2 = 87; 223 + 4 = 227.
- 2nd α decay: 83 + 2 = 85; 227 + 4 = 231.
- 3rd α decay: 81 + 2 = 83; 231 + 4 = 235.
- For each α decay, reduce atomic number by 2 and mass by 4:
So we start with an isotope that has a mass of 235 and an atomic number of 81, which corresponds to Astatine-210. It might seem complicated, but tracing backward through the decays correctly identifies that the initial isotope potentially could be one that decays to Francium-223.
Conclusion
Among the options provided, Astatine-210 will yield Francium-223 after undergoing three alpha and two beta decays.
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