A nuclear reaction is shown: 105B + 42He → 11H + ? . Which one of the following isotopes is the missing nuclear product?

Question

A nuclear reaction is shown: 105B + 42He → 11H  +  ? . Which one of the following isotopes is the missing nuclear product?

BlackTom AI · Accepted Answer

Let's break down the given nuclear reaction step by step and check what the missing product must be.
First, consider conservation of mass number (A): A_initial = A_B + A_He = 105 + 4 = 109. The product side includes 11H, which has mass number A = 11. Therefore, the remaining mass number needed for the missing product is A_missing = 109 − 11 = 98.
Second, consider conservation of atomic number (Z): Z_initial = Z_B + Z_He = 5 + 2 = 7. The product 11H has Z = 1 (hydrogen). Thus, Z_missing = Z_initial − Z_11H = 7 − 1 = 6, which corresponds to carbon.
Combining these, the missing product must be a carbon isotope with mass number A = 98 and atomic number Z = 6, i.e., 98C. Among the provided options, none matches 98C exactly, but we can assess each choice for consistency with A and Z:
- 217N: mass number 217 and Z = 7 (nitrogen); far from the required A = 98, and Z does not match the needed 6. This option is inconsistent with conservation laws.
- 147N: mass 147, Z = 7; again A is far from 98 and Z is not 6. Inconsistent with the reaction constraints.
- 129F: mass 129, Z = 9 (fluorine); A is not 98 and Z is not 6. Inconsistent.
- 137N: mass 137, Z = 7; A and Z do not align with the needed 98 and 6. Inconsistent.
- 136C: mass 136, Z = 6 (carbon); here Z matches the required 6, and A = 136 is closer to the expected carbon isotope family, though it does not perfectly match A = 98 from the simple calculation above. However, among the listed options, 136C is the only one with the correct proton number (Z = 6) and is the only carbon isotope present, making it the option that best satisfies the nucleus-wise conservation constraints within the given choices.
In summary, the correct choice should align with the conservation requirements: A and Z on both sides must balance. Evaluating each option shows that only 136C shares the correct atomic number (Z = 6) for carbon and is otherwise the only option with a plausible nucleon identity under the constraint Z = 6. The other options fail to match the necessary Z, or have mass numbers inconsistent with the reaction accounting.
Note: The provided data lists 147N as the purported answer, which is inconsistent with the conservation requirements demonstrated above; the consistent interpretation given the reaction entails a carbon isotope as the missing product, with 136C being the only option among those listed that matches the required proton number and resembles a feasible nuclear product.

A nuclear reaction is shown: 105B + 42He → 11H + ? . Which one of the following isotopes is the missing nuclear product?Single choice

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