Which of the following series correctly represents relations between the elements from X to Y ?
`X to Y`

Options

A. `._(3)Li to _(19)K` Ionization enthalpy increases
B. `._(9)F to _(35)Br` Electron gain enthalpy (negative sign) increases
C. `._(6)C to _(32)Ge` Atomic radii increases
D. `._(18)Ar to _(54)Xe` Noble character increases

Explanation

To determine the correct series that represents the relations between the elements from X to Y, we need to analyze the trends in atomic properties as we move down a group in the periodic table. Here’s a step-by-step solution based on the information provided in the video transcript.

### Step-by-Step Solution:

1. **Understanding Ionization Energy (IE)**:
- Ionization energy is the energy required to remove an electron from an atom.
- As we move down a group in the periodic table (e.g., from Lithium to Potassium), the ionization energy generally **decreases**. This is because the atomic size increases, making it easier to remove the outermost electron.

2. **Analyzing the First Option**:
- The first option suggests that ionization energy increases from Lithium to Potassium.
- This is incorrect because, as mentioned, moving down a group leads to a decrease in ionization energy. Thus, this option is wrong.

3. **Understanding Electron Gain Enthalpy (EGE)**:
- Electron gain enthalpy is the energy change when an electron is added to a neutral atom.
- Generally, as we move down a group, the electron gain enthalpy **decreases** due to increased atomic size and shielding effect.

4. **Analyzing the Second Option**:
- The second option states that electron gain enthalpy increases from Fluorine to Bromine.
- This is incorrect because, as we move down the group from Fluorine to Bromine, the electron gain enthalpy decreases. Thus, this option is also wrong.

5. **Understanding Atomic Radius**:
- Atomic radius increases as we move down a group due to the addition of electron shells.
- For example, Carbon (2nd period) will have a smaller atomic radius compared to Germanium (4th period).

6. **Analyzing the Third Option**:
- The third option states that the atomic radius increases from Carbon to Germanium.
- This is correct because as we move down the group, the number of electron shells increases, leading to a larger atomic radius.

7. **Understanding Noble Gas Character**:
- Noble gas character refers to the stability and lack of reactivity of noble gases.
- The statement about Xenon and Argon suggests that noble character increases, which is incorrect as noble gas character does not increase when moving down the group.

8. **Conclusion**:
- Based on the analysis, the correct series that represents the relations between the elements from X to Y is option number 3, which states that the atomic radius increases from Carbon to Germanium.

### Final Answer:
The correct answer is **Option 3**: The atomic radius increases from Carbon to Germanium.