For the electrons of oxygen atom, which of the following statements is correct? (1) \(Z_{\text {ett }}\) for an electron in a 2s orbital is the same as \(Z_{\text {eft }}\) for an electron in a 2p orbital. (2) An electron in the 2 s orbital has the same energy as an electron in the \(2 p\) orbital. (3) \(\mathrm{Z}_{\mathrm{efl}}\) for an electron in a 1 s orbital is the same as \(Z_{\text {etf }}\) for an electron in a 2 s orbital. (4) The two electrons present in the 2 s orbital have different spin quantum numbers \(\left(m_{s}\right)\).

The Effective Nuclear Charge, often symbolized as \(Z_\text{eff}\), represents the net positive charge that an electron experiences within an atom. This concept is crucial for understanding electron interactions and overall atomic structure.
The nucleus is composed of positively charged protons. However, in a multi-electron atom, electrons repel each other. Outer electrons are less attracted to the nucleus compared to inner electrons because outer electrons experience a shielding effect.
The shielding effect is the reduction in the effective nuclear charge by the inner-shell electrons. Inner-shell electrons block some of the positive charge from reaching the outer electrons.
Thus, outer electrons experience a net positive charge that is less than the actual charge of the nucleus, and we call this the Effective Nuclear Charge. The formula often used to estimate it is:
\[ Z_{\text{eff}} = Z - S \]where:

• \(Z\) is the total number of protons, or the actual nuclear charge
• \(S\) is the average number of electrons between the nucleus and the electron in question, or the shielding constant

Electrons in different orbitals will experience different effective nuclear charges due to variations in their shielding and penetration capabilities.

Electron orbitals describe regions in an atom where electrons are likely to be found. These regions differ based on energy levels and shapes.
Each orbital can hold a specific number of electrons and has a unique shape and orientation.
Orbitals are organized into different shells (energy levels), with each shell containing one or more subshells: s, p, d, and f. Here are some key points to understand:

• **1s orbital:** Spherical and closest to the nucleus. Holds up to 2 electrons.
• **2s orbital:** Also spherical but larger in size. Holds up to 2 electrons in the second energy level.
• **2p orbitals:** Dumbbell-shaped and oriented in three directions (x, y, z). Each can hold up to 2 electrons, for a total of 6 across the three orbitals in the second energy level.

While 2s and 2p orbitals are in the same energy level (n=2), they differ in energy due to their shapes and orientations. 2s is typically lower in energy because it penetrates closer to the nucleus, experiencing less shielding compared to 2p orbitals.
The rules of orbital filling follow specific principles:

• **Aufbau Principle:** Orbitals are filled from lowest to highest energy levels.
• **Pauli Exclusion Principle:** No two electrons can have the same set of quantum numbers within an atom.
• **Hund’s Rule:** Electrons will fill degenerate orbitals (same energy) singly before pairing up.

These principles help describe the electron configuration and the probable locations and energies of an atom’s electrons.

The spin quantum number, symbolized as \(m_{s}\), is a quantum number that describes the intrinsic angular momentum (also known as spin) of an electron within an orbital.
Unlike other quantum numbers (n, l, m_l), which describe the spatial distribution and energy of an electron’s orbit, the spin quantum number specifies the direction of an electron’s spin.
The spin quantum number can have only one of two possible values:

• \( +\frac{1}{2} \) – Called 'spin up'
• \( -\frac{1}{2} \) – Called 'spin down'

This concept is vital because of the Pauli Exclusion Principle, which states that no two electrons in the same atom can have the same set of four quantum numbers (n, l, m_l, and \(m_{s}\)).
As a result, if an orbital holds two electrons, their spins must be opposite to comply with this principle. This explains why electrons in a fully-occupied orbital have opposite spins. For instance, if one electron in the 2s orbital has a spin quantum number \( +\frac{1}{2} \), the other must have \( -\frac{1}{2} \).
This balanced spinning creates a paired state, stabilizing the atom and contributing to the magnetic properties of the material.
In summary, understanding spin quantum numbers helps in comprehending electron configurations and the physical properties of elements.