To solve this problem of nuclear fusion involving a reaction between Nitrogen ([tex]\(_{7}^{14}N\)[/tex]) and Hydrogen ([tex]\(_{1}^{1}H\)[/tex]), we must identify the resulting Carbon nucleus in the form [tex]\(_{B}^{A}C\)[/tex].
### Step-by-Step Solution:
1. Identify the components of each element:
- Nitrogen ([tex]\(_{7}^{14}N\)[/tex]):
- Atomic number (number of protons) = 7
- Mass number = 14
- Number of neutrons = Mass number - Atomic number = 14 - 7 = 7
- Hydrogen ([tex]\(_{1}^{1}H\)[/tex]):
- Atomic number (number of protons) = 1
- Mass number = 1
- Number of neutrons = Mass number - Atomic number = 1 - 1 = 0
2. Calculate the total number of protons and neutrons after the reaction:
- Total number of protons (Z):
[tex]\[
7 \, (\text{protons from } N) + 1 \, (\text{proton from } H) = 8
\][/tex]
- Total number of neutrons (N):
[tex]\[
7 \, (\text{neutrons from } N) + 0 \, (\text{neutrons from } H) = 7
\][/tex]
3. Determine the mass number (A) and atomic number (B) of the resulting nucleus:
- Mass number (A) = Total number of protons + Total number of neutrons
[tex]\[
A = 8 \, (\text{protons}) + 7 \, (\text{neutrons}) = 15
\][/tex]
- Atomic number (B) = Total number of protons
[tex]\[
B = 8
\][/tex]
4. Identify the element with atomic number 8:
- The element with atomic number 8 is Oxygen ([tex]\(_{8}C\)[/tex]).
### Final Reaction:
Based on these calculations, the nuclear fusion equation becomes:
[tex]\[
_{7}^{14}\text{N} + _{1}^{1}\text{H} \rightarrow _{8}^{15}\text{C}
\][/tex]
Thus, the values for [tex]\(A\)[/tex] and [tex]\(B\)[/tex] and the resulting element [tex]\(C\)[/tex] are:
- [tex]\(A\)[/tex]: 15
- [tex]\(B\)[/tex]: 8
- [tex]\(C\)[/tex]: Oxygen ([tex]\(O\)[/tex]).
