An unknown stable nuclide after absorbing a neutron emits an electron, and the new nuclide splits spontaneously into two alpha particles. The unknown nuclide is :

Options

A. `._(4)Be^(9)`
B. `._(3)Li^(7)`
C. `._(2)He^(4)`
D. `._(5)B^(10)`

Explanation

To solve the problem, we need to analyze the nuclear reactions step by step.

### Step 1: Identify the initial nuclide
Let’s denote the unknown stable nuclide as \( X \) with atomic number \( Z \) and mass number \( A \). Therefore, we can represent it as \( _Z^A X \).

### Step 2: Absorption of a neutron
When this nuclide absorbs a neutron, it transforms into a new nuclide. The neutron has no charge and a mass number of 1. The reaction can be represented as:
\[ _X^A + _0^1 n \rightarrow _Z^{A+1} Y \]
where \( Y \) is the new nuclide formed after neutron absorption.

### Step 3: Emission of an electron
The new nuclide \( Y \) then emits an electron (beta decay). The emission of an electron changes the atomic number by -1 (since an electron has a charge of -1). The reaction can be represented as:
\[ _Z^{A+1} Y \rightarrow _{Z-1}^{A+1} Z' + _{-1}^0 e \]
where \( Z' \) is the resulting nuclide after the emission of the electron.

### Step 4: Splitting into two alpha particles
The nuclide \( Z' \) then splits spontaneously into two alpha particles. Each alpha particle has an atomic number of 2 and a mass number of 4. The reaction can be represented as:
\[ _{Z-1}^{A+1} Z' \rightarrow 2 \times _2^4 He \]

### Step 5: Balancing the equation
To find the original nuclide \( X \), we need to balance the atomic numbers and mass numbers on both sides of the equation.

1. **Balancing mass numbers**:
\[ A + 1 = 2 \times 4 \]
\[ A + 1 = 8 \implies A = 7 \]

2. **Balancing atomic numbers**:
\[ Z = 2 \times 2 + 1 \]
\[ Z = 4 + 1 \implies Z = 5 \]

### Step 6: Identifying the nuclide
The nuclide with atomic number 3 and mass number 7 is Lithium (\( _3^7 Li \)).

### Conclusion
Thus, the unknown stable nuclide is Lithium.

### Final Answer
The unknown stable nuclide is \( _3^7 Li \).

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