For the fission reaction
`._(92)U^(235) + ._(0)n^(1) rarr ._(56)Ba^(140) + ._(y)E^(x) + 2 ._(0)n^(1)`
The value of x and y will be

Options

A. `x = 93 and y = 34`
B. `x = 92 and y = 35`
C. `x = 89 and y = 44`
D. `x = 94 and y = 36`

Explanation

To solve the fission reaction given by:

\[ _{92}^{235}U + _{0}^{1}n \rightarrow _{56}^{140}Ba + _{y}^{x}E + 2_{0}^{1}n \]

we need to determine the values of \(x\) and \(y\).

### Step 1: Calculate the total mass before the reaction
The total mass before the reaction consists of the mass of uranium and the neutron:

\[ \text{Total mass before} = 235 + 1 = 236 \]

### Step 2: Calculate the total mass after the reaction
The total mass after the reaction includes the mass of barium, the unknown element \(E\), and the two neutrons:

\[ \text{Total mass after} = 140 + x + 2 \times 1 = 140 + x + 2 = 142 + x \]

### Step 3: Set up the mass balance equation
We can equate the total mass before and after the reaction:

\[ 236 = 142 + x \]

### Step 4: Solve for \(x\)
Rearranging the equation gives us:

\[ x = 236 - 142 = 94 \]

### Step 5: Calculate the total charge before the reaction
The total charge before the reaction is the charge of uranium plus the charge of the neutron:

\[ \text{Total charge before} = 92 + 0 = 92 \]

### Step 6: Calculate the total charge after the reaction
The total charge after the reaction includes the charge of barium, the charge of the unknown element \(E\), and the charge of the two neutrons:

\[ \text{Total charge after} = 56 + y + 2 \times 0 = 56 + y \]

### Step 7: Set up the charge balance equation
We can equate the total charge before and after the reaction:

\[ 92 = 56 + y \]

### Step 8: Solve for \(y\)
Rearranging the equation gives us:

\[ y = 92 - 56 = 36 \]

### Conclusion
Thus, the values of \(x\) and \(y\) are:

\[ x = 94, \quad y = 36 \]

### Final Answer
The final answer is \(x = 94\) and \(y = 36\).

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