The given equation represents a nuclear fission process. To find the missing parts of the equation, we need to ensure conservation of both atomic numbers (protons) and mass numbers (nucleons).
We start with uranium-235 [tex]\(_{92}^{235}U\)[/tex] and a neutron [tex]\(_0^1n\)[/tex] on the left side of the equation:
[tex]\[
_{92}^{235}U + _0^1n \rightarrow_{56}^{139}Ba + \square + 3_0^1n
\][/tex]
### Conservation of Mass Number:
The mass number (A) on the left side is 235 (uranium) + 1 (neutron) = 236.
On the right side, we have:
- Barium: [tex]\(_{56}^{139}Ba\)[/tex], which contributes 139.
- 3 neutrons: Each with a mass number of 1, so 3 × 1 = 3.
Let's denote the mass number of the unknown nucleus [tex]\(_Z^AC\)[/tex] as [tex]\(A\)[/tex]. Hence, we have:
[tex]\[
139 + A + 3 = 236
\][/tex]
Solving for [tex]\(A\)[/tex]:
[tex]\[
A = 236 - 139 - 3 = 94
\][/tex]
### Conservation of Atomic Number:
The atomic number (Z) on the left side is 92 (uranium) + 0 (neutron) = 92.
On the right side:
- Barium: [tex]\(Z = 56\)[/tex]
- The unknown nucleus has an atomic number [tex]\(Z\)[/tex].
- 3 neutrons contribute 0 to the atomic number.
So,
[tex]\[
56 + Z = 92
\][/tex]
Solving for [tex]\(Z\)[/tex]:
[tex]\[
Z = 92 - 56 = 36
\][/tex]
The element with atomic number 36 is Krypton ([tex]\(_{36}\text{Kr}\)[/tex]).
Therefore, the unknown nucleus is:
[tex]\[
_{36}^{94}Kr
\][/tex]
### Complete Equation:
The complete nuclear fission equation is:
[tex]\[
_{92}^{235}U + _0^1n \rightarrow_{56}^{139}Ba + _{36}^{94}Kr + 3_0^1n
\][/tex]
By ensuring conservation of both mass number and atomic number, the answer is verified. The spaces can now be filled as follows:
- A: [tex]\(139\)[/tex]
- B: [tex]\(94\)[/tex]
- C: [tex]\(3\)[/tex]
To sum up the result:
[tex]\[
A: \; 139, \quad B: \; 94, \quad C: \; 3
\][/tex]
