Use the periodic table to complete each nuclear fusion equation.
${ }_1^2 H +{ }_1^3 H \rightarrow{ }_B^A He$
${ }_7^{14} N+{ }_1^1 H \rightarrow{ }_D^{ C } E$
A: $\square$ C: $\square$
B: $\square$ D: $\square$
E: $\square$
Answer (2)
The answers for the nuclear fusion equations are A = 5, B = 2, C = 15, D = 8, and E is Oxygen (O). The first equation reflects the fusion of deuterium and tritium to form helium, while the second equation shows the fusion of nitrogen and hydrogen to produce oxygen. In summary, the complete equations are 1 2 H + 1 3 H → 2 5 He and 7 14 N + 1 1 H → 8 15 O .
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Calculate A by summing the mass numbers of the reactants in the first equation: A = 2 + 3 = 5 .
Calculate B by summing the atomic numbers of the reactants in the first equation: B = 1 + 1 = 2 .
Calculate C by summing the mass numbers of the reactants in the second equation: C = 14 + 1 = 15 .
Calculate D by summing the atomic numbers of the reactants in the second equation: D = 7 + 1 = 8 , and identify element E as Oxygen (O).
The final answers are: A = 5 , B = 2 , C = 15 , D = 8 , and E = O , so the answer is A = 5 , B = 2 , C = 15 , D = 8 , E = O .
Explanation
Problem Analysis We are given two nuclear fusion equations to complete using the periodic table. The goal is to find the missing mass numbers (A and C), atomic numbers (B and D), and the element symbol (E). We will use the conservation of mass number and atomic number in nuclear reactions to find these values.
Completing the First Equation For the first equation, 1 2 H + 1 3 H i g h t ha r p oo n u p B A He , we need to find A and B. The mass number A is the sum of the mass numbers of the reactants, which are 2 and 3. Therefore, A = 2 + 3 = 5. The atomic number B is the sum of the atomic numbers of the reactants, which are 1 and 1. Therefore, B = 1 + 1 = 2.
Result of the First Equation Thus, the first equation is 1 2 H + 1 3 H i g h t ha r p oo n u p 2 5 He . So, A = 5 and B = 2.
Completing the Second Equation For the second equation, 7 14 N + 1 1 H i g h t ha r p oo n u p D C E , we need to find C, D, and E. The mass number C is the sum of the mass numbers of the reactants, which are 14 and 1. Therefore, C = 14 + 1 = 15. The atomic number D is the sum of the atomic numbers of the reactants, which are 7 and 1. Therefore, D = 7 + 1 = 8.
Result of the Second Equation The element with atomic number 8 is Oxygen (O). So the second equation is 7 14 N + 1 1 H i g h t ha r p oo n u p 8 15 O . Thus, C = 15, D = 8, and E = O.
Final Answer In summary: A = 5, B = 2, C = 15, D = 8, and E = O.
Examples
Nuclear fusion is a process that powers the sun and other stars. Understanding how to balance nuclear equations is crucial in fields like astrophysics and nuclear engineering. For example, scientists use these principles to study the energy production in stars or to design nuclear reactors for power generation. By ensuring that the number of protons and neutrons is conserved, we can predict the products of nuclear reactions and calculate the energy released.
