When nucleus of an electrically neutral atom undergoes a radioactive decay process, it will remain neutral after the decay if the process is
(a) An `alpha`- decay (b) `A beta^(o+)`-decay
(c ) `A gamma`-decay (d) `A K`- capture process

Options

A. An `alpha`-decay
B. `A gamma`-decay
C. `A K`-capture process
D. `A beta`-decay

Explanation

To solve the question regarding which radioactive decay process allows an electrically neutral atom to remain neutral after the decay, we will analyze each of the four processes mentioned: alpha decay, beta decay, gamma decay, and K-capture.

### Step-by-Step Solution:

1. **Understanding Alpha Decay**:
- In alpha decay, the nucleus emits an alpha particle, which is a helium nucleus (2 protons and 2 neutrons).
- This results in a decrease of 2 in the atomic number (Z) and a decrease of 4 in the atomic mass (A).
- Since the atomic number decreases, the atom becomes a different element and loses 2 positive charges, thus it will not remain neutral.
- **Conclusion**: Alpha decay does not keep the atom neutral.

2. **Understanding Beta Decay**:
- In beta decay (specifically β+ decay), a proton in the nucleus is converted into a neutron, emitting a positron (β+ particle) and a neutrino.
- This process decreases the atomic number by 1 (since a proton is lost) but does not change the atomic mass.
- The emission of a positron means that the atom loses a positive charge, thus it will not remain neutral.
- **Conclusion**: Beta decay does not keep the atom neutral.

3. **Understanding Gamma Decay**:
- Gamma decay involves the emission of gamma radiation (high-energy photons) from an excited nucleus.
- There is no change in the atomic number or atomic mass during this process.
- Since there is no change in the number of protons or neutrons, the overall charge of the atom remains the same.
- **Conclusion**: Gamma decay keeps the atom neutral.

4. **Understanding K-Capture**:
- K-capture is a process where an electron from the K shell (closest to the nucleus) is captured by the nucleus, converting a proton into a neutron.
- This process decreases the atomic number by 1 (as a proton is lost) and does not change the atomic mass.
- The atom loses a positive charge (due to the loss of a proton), thus it will not remain neutral.
- **Conclusion**: K-capture does not keep the atom neutral.

### Final Answer:
After analyzing all four processes, the only decay process that allows the electrically neutral atom to remain neutral after the decay is **(c) A gamma decay**.

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