Chapter 16: Problem 87

Complete this fusion reaction: ${ }_{4}^{8} \mathrm{Be}+{ }_{2}^{4} \mathrm{He} \rightarrow ?+\gamma$

Short Answer

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The short answer is: ${ }_{4}^{8} \mathrm{Be}+{ }_{2}^{4} \mathrm{He} \rightarrow { }_{6}^{12} \mathrm{C}+\gamma$

Step by step solution

Analyze given information

In the given fusion reaction: $${ }_{4}^{8} \mathrm{Be}+{ }_{2}^{4} \mathrm{He} \rightarrow ?+\gamma$$ We have Beryllium-8 (${ }_{4}^{8} \mathrm{Be}$) and Helium-4 (${ }_{2}^{4} \mathrm{He}$) as the reactants, and a gamma photon ($\gamma$) and an unknown product as the products.

Conservation of Atomic Number (Z)

The conservation of atomic number (Z) states that the sum of atomic numbers of the reactants must be equal to the sum of atomic numbers of the products. In our case: $$Z_\text{reactants} = Z_\text{products}$$ From the given reaction, the total atomic number of reactants is: $$Z_\text{reactants} = 4 + 2 = 6$$ On the product side, the atomic number of a gamma photon is 0. So, the atomic number of the unknown product must be 6 to obey the conservation of atomic number (Z).

Conservation of Mass Number (A)

The conservation of mass number (A) states that the sum of mass numbers of the reactants must be equal to the sum of mass numbers of the products. In our case: $$A_\text{reactants} = A_\text{products}$$ From the given reaction, the total mass number of reactants is: $$A_\text{reactants} = 8 + 4 = 12$$ On the product side, the mass number of a gamma photon is 0. So, the mass number of the unknown product must be 12 to obey the conservation of mass number (A).

Identify the unknown product

Based on the conservation laws, the unknown product must have an atomic number (Z) of 6 and a mass number (A) of 12. An element with an atomic number of 6 is Carbon (C). So, the missing product is Carbon-12: $${ }_{6}^{12} \mathrm{C}$$

Complete the fusion reaction

With the identification of the unknown product as Carbon-12 (${ }_{6}^{12} \mathrm{C}$), we can now complete the given fusion reaction: $${ }_{4}^{8} \mathrm{Be}+{ }_{2}^{4} \mathrm{He} \rightarrow { }_{6}^{12} \mathrm{C}+\gamma$$

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Complete this fusion reaction: \({ }_{4}^{8} \mathrm{Be}+{ }_{2}^{4} \mathrm{He} \rightarrow ?+\gamma\)

Short Answer

Step by step solution

Analyze given information

Conservation of Atomic Number (Z)

Conservation of Mass Number (A)

Identify the unknown product

Complete the fusion reaction

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