Assertion (A): `IE_(1)` of `N` is lower than `O`.
Reason (R ) : Across a period `Z_(eff)` decrease.

Options

A. If both Assertion (A) and (R ) are correct and Reason (R ) is the correct explanation of Assertion (A).
B. If both (A) and (R ) are correct but (R ) is not the correct explanation for (A).
C. If (A) is correct but (R ) is not correct.
D. If both (A) and (R ) are correct

Explanation

To analyze the given assertion and reason, we will break down the concepts of ionization energy and effective nuclear charge.

### Step-by-Step Solution:

1. **Understanding Ionization Energy (IE)**:
- Ionization energy is defined as the energy required to remove an electron from the outermost shell of a neutral gaseous atom.
- Higher ionization energy indicates that it is more difficult to remove an electron.

2. **Electron Configuration of Nitrogen and Oxygen**:
- Nitrogen (N) has the electron configuration of \(1s^2 2s^2 2p^3\).
- Oxygen (O) has the electron configuration of \(1s^2 2s^2 2p^4\).

3. **Stability of Half-filled Configuration**:
- Nitrogen has a half-filled p-orbital configuration (2p^3), which is relatively stable. This stability makes it harder to remove an electron from nitrogen.
- Oxygen, on the other hand, has one more electron in the p-orbital (2p^4), which makes it less stable than nitrogen when it comes to losing an electron.

4. **Comparing Ionization Energies**:
- Due to the half-filled stability, nitrogen has a higher ionization energy compared to oxygen. Therefore, the assertion that the ionization energy of nitrogen (IE1 of N) is lower than that of oxygen (IE1 of O) is incorrect.

5. **Understanding Effective Nuclear Charge (Z_eff)**:
- Effective nuclear charge is the net positive charge experienced by electrons in the outer shell.
- As we move across a period from left to right, the number of protons increases while the shielding effect remains relatively constant, leading to an increase in effective nuclear charge.

6. **Assertion and Reason Analysis**:
- The assertion (A) is incorrect because the ionization energy of nitrogen is actually higher than that of oxygen.
- The reason (R) is also incorrect because effective nuclear charge (Z_eff) increases across a period, not decreases.

### Conclusion:
Both the assertion and the reason provided in the question are incorrect.