In a nuclear decay
`""_(Z)X^(A) to ""_(z-1)M^(A-4) to ""_(z-2)N^(A-4)`
the particles emitted are in sequence:

Options

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

Explanation

To solve the problem of identifying the sequence of particles emitted during the nuclear decay process described, we can break it down step by step.

### Step-by-Step Solution:

1. **Identify the Initial Nucleus**:
The initial nucleus is represented as \( _{Z}X^{A} \). Here, \( Z \) is the atomic number (number of protons) and \( A \) is the mass number (total number of protons and neutrons).

2. **First Decay Process**:
The first decay transforms \( _{Z}X^{A} \) into \( _{Z-1}M^{A-4} \). This indicates that during this decay:
- The atomic number decreases by 1 (indicating the emission of a particle that reduces the charge).
- The mass number decreases by 4.

Since the mass number decreases by 4 and the atomic number decreases by 1, we can conclude that an alpha particle (\( _{2}^{4}\alpha \)) is emitted. The alpha particle consists of 2 protons and 2 neutrons.

3. **Second Decay Process**:
The next transformation is from \( _{Z-1}M^{A-4} \) to \( _{Z-2}N^{A-4} \). Here, the atomic number decreases by 1 again, but the mass number remains the same (A-4).
- Since the atomic number decreases by 1, this indicates that a beta particle is emitted. In this case, it is a beta minus decay, where a neutron is converted into a proton, emitting an electron (beta particle).

4. **Final Decay Process**:
The final transformation is from \( _{Z-2}N^{A-4} \) to \( _{Z-2}N^{A-4} \) with no change in mass number. This indicates that another beta particle is emitted, but this time it is a beta plus decay, where a proton is converted into a neutron, emitting a positron (beta plus particle).

5. **Sequence of Emitted Particles**:
Based on the above transformations, the sequence of particles emitted during the nuclear decay process is:
- First: Alpha particle (\( \alpha \))
- Second: Beta minus particle (\( \beta^- \))
- Third: Beta plus particle (\( \beta^+ \))

### Final Answer:
The sequence of particles emitted is: **Beta minus, Alpha, Beta plus**.

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