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

We are given four options and need to determine which one correctly represents the periodic trend from element X to element Y. Let's analyze each option step by step, recalling the periodic trends:

Option A: $$_3$$Li → $$_{19}$$K and ionization enthalpy increases.

Lithium (Li) and Potassium (K) are both in Group 1 (alkali metals). Li is in Period 2, and K is in Period 4. As we move down a group, the atomic size increases due to the addition of electron shells. The increased distance between the nucleus and the outermost electron reduces the effective nuclear attraction, making it easier to remove an electron. Therefore, ionization enthalpy decreases down the group. From Li to K, ionization enthalpy decreases, not increases. Thus, Option A is incorrect.

Option B: $$_9$$F → $$_{35}$$Br and electron gain enthalpy (negative sign) increases.

Fluorine (F) and Bromine (Br) are both in Group 17 (halogens). F is in Period 2, and Br is in Period 4. Electron gain enthalpy is the energy change when an electron is added to an atom; a more negative value indicates greater energy release (higher tendency to gain an electron). Down the group, atomic size increases, and the incoming electron is farther from the nucleus, reducing the effective nuclear attraction. This causes the electron gain enthalpy to become less negative (i.e., the numerical value increases toward zero). For example, F has an electron gain enthalpy of approximately -328 kJ/mol, and Br has approximately -324 kJ/mol. The negative sign decreases in magnitude (from -328 to -324), meaning it becomes less negative. The option states that the negative sign increases, implying it becomes more negative, which is incorrect. Therefore, Option B is incorrect.

Option C: $$_6$$C → $$_{32}$$Ge and atomic radii increases.

Carbon (C) and Germanium (Ge) are both in Group 14. C is in Period 2, and Ge is in Period 4. Down the group, each successive element has an additional electron shell, leading to an increase in atomic size. The atomic radius of C is approximately 70 pm (covalent radius), and Ge is approximately 120 pm. Thus, atomic radii increase from C to Ge. Therefore, Option C is correct.

Option D: $$_{18}$$Ar → $$_{54}$$Xe and noble character increases.

Argon (Ar) and Xenon (Xe) are both in Group 18 (noble gases). Ar is in Period 3, and Xe is in Period 5. Noble character refers to chemical inertness and stability, which is highest for elements with high ionization enthalpy and low reactivity. Down the group, atomic size increases, and ionization enthalpy decreases due to the increased distance from the nucleus. This makes the heavier noble gases less stable and more reactive. For instance, Xe can form compounds (like XeF₂), while Ar does not form stable compounds under normal conditions. Thus, noble character decreases down the group. From Ar to Xe, noble character decreases, not increases. Therefore, Option D is incorrect.

After evaluating all options, only Option C correctly represents the trend. Hence, the correct answer is Option C.