In the radioactive decay of `""_(Z)X^(A)`, which of the following could be considered as incorrect statement?

Options

A. `alpha`-decay involves the decrease of both A and Z by 2
B. `beta`-dacay involves the increase of Z by one, A remaining constant
C. K-electron capture results in the decrease of Z by one with no change in A and emission of `gamma`- rays
D. `gamma`- ray emission is followed by the emission of `alpha` or `beta` - particles

Answer

To solve the question regarding the incorrect statement in the radioactive decay of `""_(Z)X^(A)`, we will analyze the four types of decay processes mentioned: alpha decay, beta decay, K electron capture, and gamma decay.

### Step-by-Step Solution:

1. **Understanding Alpha Decay**:
- In alpha decay, a helium nucleus (alpha particle) is emitted from the parent nucleus.
- The mass number (A) decreases by 4 (because an alpha particle has a mass number of 4) and the atomic number (Z) decreases by 2.
- Therefore, the statement regarding alpha decay that says both A and Z decrease by 2 is incorrect.

2. **Understanding Beta Decay**:
- In beta decay, a neutron in the nucleus is converted into a proton, and an electron (beta particle) is emitted.
- The atomic number (Z) increases by 1, while the mass number (A) remains constant.
- Thus, the statement that Z increases by 1 and A remains constant is correct.

3. **Understanding K Electron Capture**:
- In K electron capture, an electron from the innermost shell is captured by the nucleus, which combines with a proton to form a neutron.
- This process decreases the atomic number (Z) by 1 while the mass number (A) remains unchanged.
- Therefore, the statement that Z decreases by 1 and A remains constant is correct.

4. **Understanding Gamma Decay**:
- In gamma decay, the nucleus releases energy in the form of gamma rays without changing the number of protons or neutrons.
- Thus, both A and Z remain unchanged.
- The statement regarding gamma decay is also correct.

### Conclusion:
Based on the analysis:
- The incorrect statement is related to alpha decay, where it was incorrectly stated that both A and Z decrease by 2. The correct decrease is A by 4 and Z by 2.

### Final Answer:
The incorrect statement is related to alpha decay, which is option 1.

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