In radioactive reaction
`._(Z)^(A)Xrarr ._(Z+1)^(A)X_(1)rarr ._(Z+2)^(A)X_(2)rarr ._(Z)^(A-4)X_(3) rarr ._(Z+1)^(A-4)X_(4)`
Successive emission of particles is

Options

A. `beta^(-), beta^(-), alpha`
B. `beta^(-), beta^(-), beta^(+), alpha`
C. `beta^(-), beta^(-),alpha, alpha`
D. `beta^(-), beta^(-), alpha, beta^(-)`

Answer

To solve the problem of identifying the successive emissions of particles in the given radioactive reaction, we can analyze the changes in atomic number (Z) and mass number (A) for each step in the reaction.

### Step-by-Step Solution:

1. **Identify the Initial Nucleus:**
The initial nucleus is represented as \( _{Z}^{A}X \).

2. **First Emission:**
The first transformation is \( _{Z}^{A}X \rightarrow _{Z+1}^{A}X_1 \).
- **Change in Atomic Number (Z):** Increases by 1.
- **Change in Mass Number (A):** No change.
- **Conclusion:** This emission is a **beta-minus particle** (β⁻), which increases the atomic number by 1 without changing the mass number.

3. **Second Emission:**
The second transformation is \( _{Z+1}^{A}X_1 \rightarrow _{Z+2}^{A}X_2 \).
- **Change in Atomic Number (Z):** Increases by 1.
- **Change in Mass Number (A):** No change.
- **Conclusion:** This emission is again a **beta-minus particle** (β⁻).

4. **Third Emission:**
The third transformation is \( _{Z+2}^{A}X_2 \rightarrow _{Z}^{A-4}X_3 \).
- **Change in Atomic Number (Z):** Decreases by 2.
- **Change in Mass Number (A):** Decreases by 4.
- **Conclusion:** This emission is an **alpha particle** (α), which decreases the atomic number by 2 and the mass number by 4.

5. **Fourth Emission:**
The fourth transformation is \( _{Z}^{A-4}X_3 \rightarrow _{Z+1}^{A-4}X_4 \).
- **Change in Atomic Number (Z):** Increases by 1.
- **Change in Mass Number (A):** No change.
- **Conclusion:** This emission is a **beta-minus particle** (β⁻) again.

### Summary of Successive Emissions:
- 1st emission: Beta-minus (β⁻)
- 2nd emission: Beta-minus (β⁻)
- 3rd emission: Alpha (α)
- 4th emission: Beta-minus (β⁻)

### Final Answer:
The successive emissions of particles are: **β⁻, β⁻, α, β⁻**.

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