Avogadro's Number: `6.022xx10^(23)`
In a thermal neutron-inducted fission process, `.^(235)U` reacts with a neturon and breaks up into energetic fragmants and (normally) `2-3` new neutrons.
We consider one single fission event: `235U+n rarr .^(137)Te+X+2n`
Identify the fragment X.

Answer

To identify the fragment \( X \) in the fission process of \( ^{235}\text{U} \) when it reacts with a neutron, we can follow these steps:

### Step 1: Write the Reaction Equation
The fission reaction can be represented as:
\[ ^{235}\text{U} + n \rightarrow ^{137}\text{Te} + X + 2n \]
where \( n \) represents a neutron.

### Step 2: Determine the Atomic Mass and Atomic Number
1. The atomic mass of \( ^{235}\text{U} \) is 235.
2. The atomic mass of the neutron \( n \) is 1.
3. Therefore, the total atomic mass before the reaction is:
\[ 235 + 1 = 236 \]

### Step 3: Calculate the Atomic Mass of Fragment \( X \)
After the fission, we have:
- The atomic mass of \( ^{137}\text{Te} \) is 137.
- There are 2 neutrons produced, each with an atomic mass of 1, contributing a total of 2 to the mass.

The total mass after the reaction is:
\[ 137 + \text{mass of } X + 2 \]
Setting the total mass before the reaction equal to the total mass after the reaction gives:
\[ 236 = 137 + \text{mass of } X + 2 \]

### Step 4: Solve for the Mass of Fragment \( X \)
Rearranging the equation:
\[ \text{mass of } X = 236 - 137 - 2 \]
Calculating this gives:
\[ \text{mass of } X = 236 - 139 = 97 \]

### Step 5: Identify the Element with Atomic Mass 97
The element with an atomic mass of 97 is Zirconium, represented as \( ^{97}\text{Zr} \).

### Final Answer
Thus, the fragment \( X \) is:
\[ X = ^{97}\text{Zr} \]