Consider the following reaction:
`""_(Z)^(A)Xto""_(Z-1)^(" "A)Yto""_(Z-1)^(A-4)Zto""_(Z-1)^(A-4)Z`
Radioactive radiation emitted in the following sequence:

Options

A. `beta, alpha,gamma`
B. `alpha,beta,gamma`
C. `gamma,beta,alpha`
D. `beta,gamma,alpha`

Explanation

To solve the problem, we need to analyze the given nuclear reactions step by step and identify the types of radioactive decay involved. The reactions are as follows:

1. \( _{Z}^{A}X \rightarrow _{Z-1}^{A}Y \)
2. \( _{Z-1}^{A}Y \rightarrow _{Z-1}^{A-4}Z \)
3. \( _{Z-1}^{A-4}Z \rightarrow _{Z-1}^{A-4}Z \)

### Step 1: Analyze the first reaction \( _{Z}^{A}X \rightarrow _{Z-1}^{A}Y \)

In this reaction, the atomic number decreases from \( Z \) to \( Z-1 \), while the mass number remains the same at \( A \). This indicates that a particle has been emitted that reduces the atomic number by 1 without changing the mass number.

**Type of Decay:** This is characteristic of **beta decay**, where a neutron is converted into a proton, and an electron (beta particle) is emitted.

### Step 2: Analyze the second reaction \( _{Z-1}^{A}Y \rightarrow _{Z-1}^{A-4}Z \)

Here, the atomic number remains the same at \( Z-1 \), but the mass number decreases from \( A \) to \( A-4 \). This suggests that a particle has been emitted that reduces the mass number by 4 without changing the atomic number.

**Type of Decay:** This is characteristic of **alpha decay**, where an alpha particle (which consists of 2 protons and 2 neutrons) is emitted.

### Step 3: Analyze the third reaction \( _{Z-1}^{A-4}Z \rightarrow _{Z-1}^{A-4}Z \)

In this reaction, both the atomic number and mass number remain unchanged. This indicates that no particles are emitted, but rather a photon is released.

**Type of Decay:** This is characteristic of **gamma decay**, where energy is released in the form of gamma radiation without changing the atomic or mass numbers.

### Summary of Decays

- First Reaction: **Beta Decay**
- Second Reaction: **Alpha Decay**
- Third Reaction: **Gamma Decay**

### Final Answer

The sequence of decays in the reactions is: **Beta, Alpha, Gamma**.

---