Complete the following nuclear equation by suppling the symbol for the other product of the fission :
`._(92)^(235)U+_(0)^(1)n rarr _(38)^(94)Sr +………+2_(0)^(1)n`

Options

A. `._(54)^(139)Xe`
B. `._(54)^(140)Xe`
C. `._(64)^(104)Gd`
D. none of these

Answer

To complete the nuclear equation given in the question, we will follow these steps:

**Step 1: Write down the initial nuclear reaction.**
The initial nuclear reaction is:
\[ _{92}^{235}U + _{0}^{1}n \rightarrow _{38}^{94}Sr + ? + 2_{0}^{1}n \]

**Step 2: Identify the known quantities.**
In this reaction:
- Uranium-235 (U) has an atomic number of 92 and a mass number of 235.
- A neutron (n) has an atomic number of 0 and a mass number of 1.
- Strontium (Sr) has an atomic number of 38 and a mass number of 94.
- Two neutrons are produced, each with an atomic number of 0 and a mass number of 1.

**Step 3: Apply conservation of atomic number.**
The total atomic number before the reaction must equal the total atomic number after the reaction.
- Before the reaction: \( 92 + 0 = 92 \)
- After the reaction: \( 38 + x + 0 \) (where \( x \) is the atomic number of the unknown product)

Setting these equal gives:
\[ 92 = 38 + x \]
Solving for \( x \):
\[ x = 92 - 38 = 54 \]

**Step 4: Apply conservation of mass number.**
The total mass number before the reaction must equal the total mass number after the reaction.
- Before the reaction: \( 235 + 1 = 236 \)
- After the reaction: \( 94 + y + 2 \) (where \( y \) is the mass number of the unknown product)

Setting these equal gives:
\[ 236 = 94 + y + 2 \]
Solving for \( y \):
\[ y = 236 - 94 - 2 = 140 \]

**Step 5: Identify the unknown product.**
Now we have determined that the unknown product has:
- Atomic number \( x = 54 \)
- Mass number \( y = 140 \)

The element with atomic number 54 is Xenon (Xe). Thus, the complete nuclear equation is:
\[ _{92}^{235}U + _{0}^{1}n \rightarrow _{38}^{94}Sr + _{54}^{140}Xe + 2_{0}^{1}n \]

**Final Answer:**
The other product of the fission is \( _{54}^{140}Xe \).

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