How to Determine the Resulting Nucleus in a Pick-Up Nuclear Reaction?

Detail Explanation:

To find the resulting nucleus in the nuclear reaction ³²He + ¹²⁶C → X + α, follow these steps:

1. First, note that an alpha (α) particle consists of 2 protons and 2 neutrons, so it can be represented as ⁴₂He.

2. Next, we'll use the conservation of nucleons (protons and neutrons) in the reaction. Add the number of protons and neutrons in the initial particles and equate it to the sum of protons and neutrons in the final particles.

3. For the initial particles, we have ³²He (2 protons and 1 neutron) and ¹²⁶C (6 protons and 6 neutrons). The total number of protons is 2 + 6 = 8, and the total number of neutrons is 1 + 6 = 7.

4. For the final particles, we have X (unknown) and α (2 protons and 2 neutrons). The total number of protons is X_protons + 2, and the total number of neutrons is X_neutrons + 2.

5. Equate the sums: X_protons + 2 = 8 and X_neutrons + 2 = 7.

6. Solve for X_protons and X_neutrons: X_protons = 6 and X_neutrons = 5.

7. Finally, combine the numbers to form the resulting isotope: ¹¹O (oxygen with 6 protons and 5 neutrons).

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