Certainly! Let's solve this problem step-by-step.
### Step-by-Step Solution:
Step 1: Write Down the Given Equation
We are given the nuclear fusion equation:
[tex]\[ {}_7^{14}N + {}_1^1H \rightarrow {}_B^A C \][/tex]
Step 2: Identify the Atomic and Mass Numbers
For the reactants:
- Nitrogen ([tex]\(N\)[/tex]) has an atomic number of 7 and a mass number of 14.
- Hydrogen ([tex]\(H\)[/tex]) has an atomic number of 1 and a mass number of 1.
Step 3: Sum the Atomic and Mass Numbers on the Left Side
Total atomic number on the left side:
[tex]\[ 7 (from~N) + 1 (from~H) = 8 \][/tex]
Total mass number on the left side:
[tex]\[ 14 (from~N) + 1 (from~H) = 15 \][/tex]
So, we need the products to also have a total atomic number of 8 and a total mass number of 15.
Step 4: Assume a Common Nuclear Fusion Product
A common product for nuclear fusion involving nitrogen and hydrogen can be oxygen ([tex]\(O\)[/tex]), which has an atomic number of 8.
Let’s assign [tex]\({}_B^A C\)[/tex] as oxygen ([tex]\(O\)[/tex]):
- Atomic number of [tex]\(C\)[/tex]: 8 (since it is oxygen [tex]\(O\)[/tex])
- Mass number of [tex]\(C\)[/tex]: We need to balance this against other products.
Step 5: Determine the Missing Element and Mass Number (B & A)
For the products to match the sum of atomic and mass numbers, we can do the following:
[tex]\[ {}_8^{15}O \rightarrow \, ? \; \, , {plausible \, elements \, hybridization\ examples(F , He \, , particle)} ({10\ range} ) \][/tex]
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