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, we will 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.
- The general reaction can be represented as:
\[ \text{X}^A_Z \rightarrow \text{Y}^{A-4}_{Z-2} + \text{He}^4_2 \]
- Here, the atomic number (number of protons) decreases by 2.
- **Conclusion**: The number of protons decreases.

**Hint**: Remember that alpha decay results in the emission of 2 protons and 2 neutrons, leading to a decrease in the atomic number.

### Step 2: Understand Beta Minus Decay
- In beta minus decay, a neutron is converted into a proton, and a beta particle (electron) is emitted.
- The reaction can be represented as:
\[ \text{X}^A_Z \rightarrow \text{Y}^{A}_{Z+1} + \beta^- + \bar{\nu} \]
- Here, the atomic number increases by 1 because a neutron is transformed into a proton.
- **Conclusion**: The number of protons increases by 1.

**Hint**: In beta minus decay, a neutron becomes a proton, leading to an increase in the atomic number.

### Step 3: Understand Beta Plus Decay
- In beta plus decay, a proton is converted into a neutron, and a beta plus particle (positron) is emitted.
- The reaction can be represented as:
\[ \text{X}^A_Z \rightarrow \text{Y}^{A}_{Z-1} + \beta^+ + \nu \]
- Here, the atomic number decreases by 1.
- **Conclusion**: The number of protons decreases.

**Hint**: Beta plus decay involves the conversion of a proton into a neutron, which reduces the atomic number.

### 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.
- The reaction can be represented as:
\[ \text{X}^A_Z + e^- \rightarrow \text{Y}^{A}_{Z-1} + \nu \]
- Here, the atomic number decreases by 1.
- **Conclusion**: There is no increase in the number of protons.

**Hint**: K-capture involves the conversion of a proton into a neutron, resulting in a decrease in the atomic number.

### Final Conclusion
After analyzing all four processes:
- **Alpha decay**: Decreases protons by 2.
- **Beta minus decay**: Increases protons by 1.
- **Beta plus decay**: Decreases protons by 1.
- **K-capture**: No change in protons.

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

### Answer
The correct option is **Beta Minus Decay** (Option B).