Problem

Complete the following nuclear reactions:

$$\begin{aligned} & {}_{7}\mathrm{N}^{14} + {}_{2}\mathrm{He}^{4} \rightarrow {}_{1}\mathrm{H}^{1} + ? \\ & {}_{5}\mathrm{B}^{11} + {}_{1}\mathrm{H}^{1} \rightarrow {}_{6}\mathrm{C}^{11} + ? \\ & {}_{3}\mathrm{Li}^{6} + ? \rightarrow {}_{4}\mathrm{Be}^{7} + {}_{0}\mathrm{n}^{1} \end{aligned}$$

Data

• Reaction 1:

$${}_{7}\mathrm{N}^{14} + {}_{2}\mathrm{He}^{4} \rightarrow {}_{1}\mathrm{H}^{1} + ?$$

Known products: Proton (${}_{1}\mathrm{H}^{1}$)
Unknown product to be determined.

• Reaction 2:

$${}_{5}\mathrm{B}^{11} + {}_{1}\mathrm{H}^{1} \rightarrow {}_{6}\mathrm{C}^{11} + ?$$

Known products: Carbon-11 (${}_{6}\mathrm{C}^{11}$)
Unknown product to be determined.

• Reaction 3:

$${}_{3}\mathrm{Li}^{6} + ? \rightarrow {}_{4}\mathrm{Be}^{7} + {}_{0}\mathrm{n}^{1}$$

Known products: Beryllium-7 (${}_{4}\mathrm{Be}^{7}$), Neutron (${}_{0}\mathrm{n}^{1}$)
Unknown reactant to be determined.

Prerequisite Concepts

1. Balancing Nuclear Reactions:
   The sum of mass numbers ($A$) and atomic numbers ($Z$) must be equal on both sides of the reaction.

2. Notation:

   • $A$: Mass number (total protons and neutrons)
   • $Z$: Atomic number (number of protons)

3. Reaction Symbols:

   • Alpha ($\alpha$): ${}_{2}\mathrm{He}^{4}$
   • Proton ($p$): ${}_{1}\mathrm{H}^{1}$
   • Neutron ($n$): ${}_{0}\mathrm{n}^{1}$
   • Deuteron ($d$): ${}_{1}\mathrm{H}^{2}$

Solution

Reaction 1:

$${}_{7}\mathrm{N}^{14} + {}_{2}\mathrm{He}^{4} \rightarrow {}_{1}\mathrm{H}^{1} + ?$$

1. Initial reactants:

$${}_{7}\mathrm{N}^{14} \quad \text{(Nitrogen-14)}, \quad {}_{2}\mathrm{He}^{4} \quad \text{(Alpha particle)}$$

2. Known product:

$${}_{1}\mathrm{H}^{1} \quad \text{(Proton)}$$

3. Determine the unknown product:
   Balance atomic and mass numbers:

   • Mass: $14 + 4 = 18 \rightarrow 1 + 17$
   • Atomic: $7 + 2 = 9 \rightarrow 1 + 8$

   Unknown product: ${}_{8}\mathrm{O}^{17} \quad \text{(Oxygen-17)}$

   Complete reaction:

$${}_{7}\mathrm{N}^{14} + {}_{2}\mathrm{He}^{4} \rightarrow {}_{1}\mathrm{H}^{1} + {}_{8}\mathrm{O}^{17}$$

---

Reaction 2:

$${}_{5}\mathrm{B}^{11} + {}_{1}\mathrm{H}^{1} \rightarrow {}_{6}\mathrm{C}^{11} + ?$$

1. Initial reactants:

$${}_{5}\mathrm{B}^{11} \quad \text{(Boron-11)}, \quad {}_{1}\mathrm{H}^{1} \quad \text{(Proton)}$$

2. Known product:

$${}_{6}\mathrm{C}^{11} \quad \text{(Carbon-11)}$$

3. Determine the unknown product:
   Balance atomic and mass numbers:

   • Mass: $11 + 1 = 12 \rightarrow 11 + 1$
   • Atomic: $5 + 1 = 6 \rightarrow 6 + 0$

   Unknown product: ${}_{0}\mathrm{n}^{1} \quad \text{(Neutron)}$

   Complete reaction:

$${}_{5}\mathrm{B}^{11} + {}_{1}\mathrm{H}^{1} \rightarrow {}_{6}\mathrm{C}^{11} + {}_{0}\mathrm{n}^{1}$$

---

Reaction 3:

$${}_{3}\mathrm{Li}^{6} + ? \rightarrow {}_{4}\mathrm{Be}^{7} + {}_{0}\mathrm{n}^{1}$$

1. Known products:

$${}_{4}\mathrm{Be}^{7} \quad \text{(Beryllium-7)}, \quad {}_{0}\mathrm{n}^{1} \quad \text{(Neutron)}$$

2. Initial reactant:

$${}_{3}\mathrm{Li}^{6} \quad \text{(Lithium-6)}$$

3. Determine the unknown reactant:
   Balance atomic and mass numbers:

   • Mass: $6 + ? = 7 + 1 \rightarrow ? = 2$
   • Atomic: $3 + ? = 4 + 0 \rightarrow ? = 1$

   Unknown reactant: ${}_{1}\mathrm{H}^{2} \quad \text{(Deuteron)}$

   Complete reaction:

$${}_{3}\mathrm{Li}^{6} + {}_{1}\mathrm{H}^{2} \rightarrow {}_{4}\mathrm{Be}^{7} + {}_{0}\mathrm{n}^{1}$$

---

Answer

1. ${}_{7}\mathrm{N}^{14} + {}_{2}\mathrm{He}^{4} \rightarrow {}_{1}\mathrm{H}^{1} + {}_{8}\mathrm{O}^{17}$
2. ${}_{5}\mathrm{B}^{11} + {}_{1}\mathrm{H}^{1} \rightarrow {}_{6}\mathrm{C}^{11} + {}_{0}\mathrm{n}^{1}$
3. ${}_{3}\mathrm{Li}^{6} + {}_{1}\mathrm{H}^{2} \rightarrow {}_{4}\mathrm{Be}^{7} + {}_{0}\mathrm{n}^{1}$