What does X stand for in the given reaction ?
`""_(20)Ca^(41) rarr ""_(20)Ca^(40)+X`.

Options

A. Proton
B. Electron
C. Neutron
D. `alpha`-particle.

Answer

To determine what X stands for in the given nuclear reaction:

\[ _{20}^{41}\text{Ca} \rightarrow _{20}^{40}\text{Ca} + X \]

we will analyze the reaction step by step.

### Step 1: Identify the Parent and Daughter Nuclei
In the reaction, we have:
- Parent nucleus: \(_{20}^{41}\text{Ca}\) (Calcium with atomic number 20 and mass number 41)
- Daughter nucleus: \(_{20}^{40}\text{Ca}\) (Calcium with atomic number 20 and mass number 40)

### Step 2: Analyze the Change in Mass Number and Atomic Number
- The mass number (A) of the parent nucleus is 41, and the mass number of the daughter nucleus is 40.
- The atomic number (Z) of both the parent and daughter nuclei is 20, which means the atomic number remains unchanged.

### Step 3: Determine the Change in Mass Number
The change in mass number from 41 to 40 indicates that there is a loss of 1 unit of mass. Therefore, we can conclude that:
\[ A_{\text{parent}} - A_{\text{daughter}} = 41 - 40 = 1 \]

### Step 4: Determine the Nature of X
Since the atomic number remains the same (Z = 20), and we have lost 1 unit of mass, we can infer that X must be a particle that has a mass number of 1 and does not change the atomic number.

### Step 5: Identify X
The only particle that fits this description is a neutron, which has a mass number of 1 and no charge (atomic number 0).

Thus, we can write:
\[ X = _{0}^{1}\text{n} \quad (\text{neutron}) \]

### Conclusion
Therefore, in the given reaction, X stands for a neutron.

### Final Answer
\[ X = \text{neutron} \]

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