To solve this nuclear fission equation, we need to ensure both atomic number (proton number) and mass number (nucleon number) are conserved. The given equation is:
[tex]\[ _{92}^{235}U + \ _{0}^1n \rightarrow \ _{56}^{139}Ba + \quad _{Z}^{A}X + 3 \ _{0}^1n \][/tex]
### Step-by-Step Solution:
1. Identify Initial Particles:
- Uranium-235 is represented as [tex]\( _{92}^{235}U \)[/tex]
- A neutron is represented as [tex]\( _{0}^1n \)[/tex]
2. Write Initial Total Mass and Atomic Numbers:
- The combined total mass number from the left side is [tex]\( 235 \)[/tex] (from Uranium) + [tex]\( 1 \)[/tex] (from the neutron) = [tex]\( 236 \)[/tex].
- The combined total atomic number from the left side is [tex]\( 92 \)[/tex] (from Uranium) + [tex]\( 0 \)[/tex] (from the neutron) = [tex]\( 92 \)[/tex].
3. Write Products' Known Particles:
- Barium-139 is represented as [tex]\( _{56}^{139}Ba \)[/tex]
- Unknown element [tex]\( _{Z}^{A}X \)[/tex] we need to determine.
- Three neutrons: [tex]\( 3 \times~_{0}^1n \)[/tex]
4. Mass Number Balance:
- Total mass number on the right: [tex]\( 139 \)[/tex] (from Barium-139) + [tex]\( A \)[/tex] (unknown element) + [tex]\( 3 \times 1 \)[/tex] (neutrons) = [tex]\( 139 + A + 3 \)[/tex].
- Since the total mass number must be conserved:
[tex]\[ 139 + A + 3 = 236 \][/tex]
[tex]\[ A = 236 - 142 \][/tex]
[tex]\[ A = 94 \][/tex]
5. Atomic Number Balance:
- Total atomic number on the right: [tex]\( 56 \)[/tex] (from Barium-139) + [tex]\( Z \)[/tex] (unknown element) + [tex]\( 3 \times 0 \)[/tex] (neutrons) = [tex]\( 56 + Z \)[/tex].
- Since the total atomic number must be conserved:
[tex]\[ 56 + Z = 92 \][/tex]
[tex]\[ Z = 92 - 56 \][/tex]
[tex]\[ Z = 36 \][/tex]
6. Determine the Unknown Element:
- According to the periodic table, element 36 is Krypton (Kr).
Thus, the nuclear fission equation with the unknown element filled in is:
[tex]\[ _{92}^{235}U + _{0}^1n \rightarrow _{56}^{139}Ba + _{36}^{94}Kr + 3 \ _{0}^1n \][/tex]
### Summary:
- A: [tex]\[ _{36}^{94}Kr \][/tex]
- B: [tex]\[ _{36}^{94}Kr \][/tex]
- C: [tex]\[ Kr \][/tex] (The chemical symbol for Krypton)
