Fill in the blank
`""_(92)U^(235) +""_(0)n^(1) to ? +""_(36)^(92)Kr + 3""_(0)^(1)n`

Options

A. `._(56)^(141)Ba`
B. `._(56)^(139)Ba`
C. `._(54)^(139)Ba`
D. `._(54)^(141)Ba`

Answer

To solve the given nuclear reaction, we need to fill in the blank with the appropriate element formed from the reaction of Uranium-235 and a neutron, which produces Krypton-92 and three neutrons. Let's break down the steps to find the missing element.

### Step-by-Step Solution:

1. **Identify the Reactants and Products**:
- Reactants: \( _{92}^{235}U + _{0}^{1}n \)
- Products: \( ? + _{36}^{92}Kr + 3 \, _{0}^{1}n \)

2. **Determine the Mass Number (A) and Atomic Number (Z)**:
- The mass number (A) is the total number of protons and neutrons.
- The atomic number (Z) is the number of protons.

3. **Calculate Total Mass Number on Reactant Side**:
- For Uranium-235: Mass number = 235
- For the neutron: Mass number = 1
- Total mass number on the reactant side = \( 235 + 1 = 236 \)

4. **Calculate Total Mass Number on Product Side**:
- For Krypton-92: Mass number = 92
- For the three neutrons: Mass number = \( 3 \times 1 = 3 \)
- Total mass number on the product side = \( 92 + 3 = 95 \)

5. **Set Up the Equation for Mass Number**:
- Let the mass number of the unknown element be \( A \).
- Therefore, we have the equation:
\[ A + 92 + 3 = 236 \]
- Simplifying gives:
\[ A + 95 = 236 \implies A = 236 - 95 = 141 \]

6. **Calculate Total Atomic Number on Reactant Side**:
- For Uranium: Atomic number = 92
- For the neutron: Atomic number = 0
- Total atomic number on the reactant side = \( 92 + 0 = 92 \)

7. **Calculate Total Atomic Number on Product Side**:
- For Krypton: Atomic number = 36
- Let the atomic number of the unknown element be \( Z \).
- Therefore, we have the equation:
\[ Z + 36 + 0 = 92 \]
- Simplifying gives:
\[ Z + 36 = 92 \implies Z = 92 - 36 = 56 \]

8. **Identify the Element**:
- The element with mass number \( A = 141 \) and atomic number \( Z = 56 \) is Barium (Ba).

### Final Answer:
The missing element is \( _{56}^{141}Ba \).

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