Consider the following decay `._(Z)^(A)Xrarr_(Z-1)^(A)Y+_(+1)^(0)e,(beta^(+))X` is unstable because:

Options

A. its nucleus has excess energy
B. `(n)/(p)` ratio is high
C. `(n)/(p)` ratio is low
D. none of these

Answer

To solve the question regarding the instability of the decay process \( _{Z}^{A}X \rightarrow _{Z-1}^{A}Y + _{+1}^{0}e \) (beta plus decay), we can break down the reasoning into several steps:

### Step 1: Understanding the Decay Process
The decay process involves a nucleus \( _{Z}^{A}X \) transforming into a nucleus \( _{Z-1}^{A}Y \) while emitting a positron \( _{+1}^{0}e \). This is characteristic of beta plus decay, where a proton is converted into a neutron, resulting in a decrease in the atomic number (Z) by one.

**Hint:** Identify the type of decay and the particles involved in the process.

### Step 2: Analyzing the Neutron-to-Proton Ratio
The stability of a nucleus is often assessed by the neutron-to-proton (n/p) ratio. For stable nuclei, this ratio tends to be close to 1 for lighter elements (atomic number < 20). As the atomic number increases, the ratio also increases due to the greater number of neutrons needed to offset the repulsive forces between protons.

**Hint:** Recall how the n/p ratio influences nuclear stability.

### Step 3: Identifying Conditions for Beta Plus Decay
Beta plus decay occurs when the n/p ratio is low. In this case, if the ratio is less than the ideal stability range, the nucleus will undergo beta plus decay to increase the n/p ratio by converting a proton into a neutron.

**Hint:** Determine the implications of a low n/p ratio on the stability of the nucleus.

### Step 4: Conclusion on Instability
Since the decay process involves the emission of a positron, it indicates that the original nucleus \( _{Z}^{A}X \) had a low n/p ratio, making it unstable. The emission of a positron helps to increase the n/p ratio, moving the nucleus toward a more stable configuration.

**Hint:** Summarize how the emission of a positron relates to the stability of the nucleus.

### Final Answer
The nucleus \( _{Z}^{A}X \) is unstable because it has a low neutron-to-proton ratio, which leads to beta plus decay as a mechanism to achieve stability by increasing the n/p ratio.