To solve the given nuclear fusion equation:
[tex]$_{7}^{14}N + {}_{1}^{1}H \rightarrow {}_{B}^{A}C$[/tex]
we need to determine the values of [tex]\(A\)[/tex], [tex]\(B\)[/tex], and the identity of the element [tex]\(C\)[/tex].
### Step 1: Determine the Mass Number (A)
The mass number [tex]\(A\)[/tex] is the sum of the mass numbers of the reacting particles:
- The mass number of nitrogen ([tex]\(N\)[/tex]) is 14.
- The mass number of hydrogen ([tex]\(H\)[/tex]) is 1.
The mass number [tex]\(A\)[/tex] of the product [tex]\(C\)[/tex] is therefore:
[tex]\[ A = 14 + 1 = 15 \][/tex]
### Step 2: Determine the Atomic Number (B)
The atomic number [tex]\(B\)[/tex] is the sum of the atomic numbers of the reacting particles:
- The atomic number of nitrogen ([tex]\(N\)[/tex]) is 7.
- The atomic number of hydrogen ([tex]\(H\)[/tex]) is 1.
The atomic number [tex]\(B\)[/tex] of the product [tex]\(C\)[/tex] is therefore:
[tex]\[ B = 7 + 1 = 8 \][/tex]
### Step 3: Determine the Identity of the Element (C)
Using the periodic table, we can find the element with atomic number [tex]\(B = 8\)[/tex]. This element is oxygen (O).
### Final Equation
With the values determined, we can now complete the fusion equation:
[tex]\[ _{7}^{14}N + {}_{1}^{1}H \rightarrow {}_{8}^{15}O \][/tex]
To summarize:
- [tex]\(A = 15\)[/tex]
- [tex]\(B = 8\)[/tex]
- [tex]\(C = O\)[/tex]
The completed equation representing the process of nuclear fusion is:
[tex]\[ _{7}^{14}N + {}_{1}^{1}H \rightarrow {}_{8}^{15}O \][/tex]
