`S_(1)` : Potential energy of the two opposite charge system increase with the decrease in distance .
`S_(2)` : When an electron makes transition from higher orbit to lower orbit it's kinetic energy increases.
`S_(3)` : When an electron make transition from lower energy to higher energy state its potential energy increases.
`S_(4)` : 11 eV photon can free an electron from 1 st excited state of `He^(+)` ion .
Select the correct set of true-false for above statements.

Options

A. `T T T T`
B. `F T T F`
C. `T F F T`
D. `F F F F`

Explanation

To solve the problem, we need to evaluate each of the four statements regarding potential energy and kinetic energy in the context of atomic physics and determine whether they are true or false.

### Step-by-Step Solution:

1. **Evaluate Statement S1:**
- The statement claims that the potential energy of a two-opposite charge system increases with a decrease in distance.
- The formula for the potential energy (U) between two opposite charges (q1 and q2) is given by:
\[ U = -\frac{k \cdot q_1 \cdot q_2}{r} \]
- Here, as the distance (r) decreases, the magnitude of U becomes more negative (i.e., it decreases), which means the potential energy is actually increasing in the negative sense (less negative).
- Therefore, **S1 is False**.

2. **Evaluate Statement S2:**
- The statement claims that when an electron transitions from a higher orbit to a lower orbit, its kinetic energy increases.
- The kinetic energy (K.E.) of an electron in an orbit is inversely proportional to the square of the principal quantum number (n):
\[ K.E. = -\frac{13.6 \, \text{eV} \cdot Z^2}{n^2} \]
- When an electron moves from a higher orbit (higher n) to a lower orbit (lower n), its kinetic energy increases because it is moving to a state with a lower n value.
- Therefore, **S2 is True**.

3. **Evaluate Statement S3:**
- The statement claims that when an electron transitions from a lower energy state to a higher energy state, its potential energy increases.
- The potential energy is also inversely proportional to the square of the principal quantum number (n):
\[ U = -\frac{13.6 \, \text{eV} \cdot Z^2}{n^2} \]
- When an electron moves from a lower energy state (lower n) to a higher energy state (higher n), the potential energy becomes less negative (increases).
- Therefore, **S3 is True**.

4. **Evaluate Statement S4:**
- The statement claims that an 11 eV photon can free an electron from the first excited state of the He⁺ ion.
- The energy required to free an electron from the first excited state (n=2) of He⁺ can be calculated as:
\[ E = -\frac{13.6 \cdot Z^2}{n^2} = -\frac{13.6 \cdot 2^2}{2^2} = -13.6 \, \text{eV} \]
- To free the electron, we need to overcome this energy, which is 13.6 eV, not 11 eV.
- Therefore, **S4 is False**.

### Summary of Statements:
- **S1:** False
- **S2:** True
- **S3:** True
- **S4:** False

### Final Answer:
The correct set of true-false for the statements is **FTTF** (False, True, True, False).