In which of the following cases, the potential energy of the given particles decreases (under the given condition)

Options

A. two proton are moving towards each other
B. one proton and one electron are moving away from each other
C. one proton and one electron move towards each other
D. two electrons are moving towards each other

Answer

To determine in which case the potential energy of the given particles decreases, we will analyze each option one by one.

### Step-by-Step Solution:

1. **Understanding Potential Energy**:
- Potential energy between charged particles depends on their charges and their distances from each other. Like charges repel and unlike charges attract.

2. **Analyzing Option 1**:
- **Case**: Two protons are moving towards each other.
- **Analysis**: Protons are positively charged and will repel each other. As they move closer, work has to be done against this repulsion, which increases the potential energy.
- **Conclusion**: Potential energy **increases**. This option is **incorrect**.

3. **Analyzing Option 2**:
- **Case**: One proton and one electron are moving away from each other.
- **Analysis**: The proton (positive charge) and the electron (negative charge) are unlike charges. When they move away from each other, the attractive force between them decreases, but no work is done since they are just moving apart without any external influence.
- **Conclusion**: Potential energy remains **constant**. This option is **incorrect**.

4. **Analyzing Option 3**:
- **Case**: One proton and one electron are moving towards each other.
- **Analysis**: The proton and electron are unlike charges and will attract each other. As they move closer, work is done by the attractive force, which decreases the potential energy.
- **Conclusion**: Potential energy **decreases**. This option is **correct**.

5. **Analyzing Option 4**:
- **Case**: Two electrons are moving towards each other.
- **Analysis**: Electrons are negatively charged and will repel each other. As they move closer, work has to be done against this repulsion, which increases the potential energy.
- **Conclusion**: Potential energy **increases**. This option is **incorrect**.

### Final Answer:
The correct option where the potential energy of the given particles decreases is when **one proton and one electron move towards each other**.