Calculate the ground state `Q` value of the induced fission raction in the equation
`n+._(92)^(235) Urarr._(92)^(236)Uastrarr._(40)^(99)Zr+._(52)^(134)Te+2n`
If the neutron is thermal. A thermal neutorn is in thermal equilibrium with its envitronmnet, it has an avergae kinetic energy given by `(3//2) kT`. Given :
`m(n) =1.0087 am u, M(.^(235)U)=235.0439) am u`,
`M(.^(99)Zr)=98.916 am u, M(.^(134)Te)=133.9115 am u`.

Explanation

To calculate the ground state Q value of the induced fission reaction given by the equation:

\[ n + _{92}^{235}U \rightarrow _{92}^{236}U \rightarrow _{40}^{99}Zr + _{52}^{134}Te + 2n \]

we will follow these steps:

### Step 1: Understand the Q value formula
The Q value of a nuclear reaction is given by the equation:

\[ Q = \Delta m \cdot c^2 \]

where \(\Delta m\) is the change in mass during the reaction, and \(c\) is the speed of light. We can also express it in terms of energy:

\[ Q = \Delta m \cdot 931.2 \text{ MeV} \]

### Step 2: Identify the masses involved in the reaction
From the problem, we have the following masses:
- Mass of neutron, \(m(n) = 1.0087 \, \text{amu}\)
- Mass of Uranium-235, \(M(^{235}U) = 235.0439 \, \text{amu}\)
- Mass of Zirconium-99, \(M(^{99}Zr) = 98.916 \, \text{amu}\)
- Mass of Tellurium-134, \(M(^{134}Te) = 133.9115 \, \text{amu}\)

### Step 3: Calculate the total mass before and after the reaction
**Before the reaction:**
- Total mass before = Mass of \(^{235}U\) + Mass of neutron
\[ \text{Total mass before} = M(^{235}U) + m(n) = 235.0439 + 1.0087 \]

**After the reaction:**
- Total mass after = Mass of \(^{99}Zr\) + Mass of \(^{134}Te\) + 2 * Mass of neutron
\[ \text{Total mass after} = M(^{99}Zr) + M(^{134}Te) + 2 \cdot m(n) \]
\[ = 98.916 + 133.9115 + 2 \cdot 1.0087 \]

### Step 4: Calculate the change in mass (\(\Delta m\))
Now, we can calculate \(\Delta m\):

\[ \Delta m = \text{Total mass before} - \text{Total mass after} \]

### Step 5: Substitute the values and calculate \(\Delta m\)
1. Calculate Total mass before:
\[ \text{Total mass before} = 235.0439 + 1.0087 = 236.0526 \, \text{amu} \]

2. Calculate Total mass after:
\[ \text{Total mass after} = 98.916 + 133.9115 + 2 \cdot 1.0087 = 98.916 + 133.9115 + 2.0174 = 234.8459 \, \text{amu} \]

3. Now calculate \(\Delta m\):
\[ \Delta m = 236.0526 - 234.8459 = 1.2067 \, \text{amu} \]

### Step 6: Calculate the Q value
Now we can substitute \(\Delta m\) into the Q value formula:
\[ Q = \Delta m \cdot 931.2 \, \text{MeV} \]
\[ Q = 1.2067 \cdot 931.2 \approx 1120.07 \, \text{MeV} \]

### Final Answer
The Q value of the induced fission reaction is approximately **1120.07 MeV**.