In which of the following processes, the number of protons in the nuleus increase ?

Options

A. `alpha`-decay
B. `beta^(-)`-decay
C. `beta^(+)`-decay
D. K - capture

Explanation

To determine in which of the following processes the number of protons in the nucleus increases, let's analyze each process step by step.

### Step 1: Understand Alpha Decay
- In alpha decay, an alpha particle (which consists of 2 protons and 2 neutrons) is emitted from the nucleus.
- This results in a decrease in the atomic number (Z) of the nucleus by 2.
- Therefore, the number of protons decreases by 2.

**Conclusion**: Alpha decay does not increase the number of protons.

### Step 2: Understand Beta Minus Decay
- In beta minus decay, a neutron in the nucleus is converted into a proton, and a beta particle (an electron) is emitted.
- This process increases the atomic number (Z) of the nucleus by 1 because a new proton is formed.

**Conclusion**: Beta minus decay increases the number of protons by 1.

### Step 3: Understand Beta Plus Decay
- In beta plus decay, a proton in the nucleus is converted into a neutron, and a positron (the beta particle) is emitted.
- This results in a decrease in the atomic number (Z) of the nucleus by 1.

**Conclusion**: Beta plus decay does not increase the number of protons.

### Step 4: Understand K-Capture
- In K-capture, an inner orbital electron is captured by the nucleus, which combines with a proton to form a neutron.
- This process also decreases the atomic number (Z) by 1, as one proton is converted into a neutron.

**Conclusion**: K-capture does not increase the number of protons.

### Final Conclusion
Among the processes discussed:
- Alpha decay: Decreases protons (not applicable)
- Beta minus decay: Increases protons (applicable)
- Beta plus decay: Decreases protons (not applicable)
- K-capture: Decreases protons (not applicable)

Thus, the process in which the number of protons in the nucleus increases is **Beta Minus Decay**.

---