Question

In multielectron atoms many of the periodic trends can be explained in terms of \(Z_{\text {eff }}\) Consider the following statements and discuss whether or not the statement is true or false. (a) Electrons in a \(p\) orbital are more effective than electrons in the \(s\) orbitals in shielding other electrons from the nuclear charge. (b) \(\mathrm{Z}_{\text {eff }}\) for an electron in an \(s\) orbital is lower than that for an electron in a \(p\) orbital in the same shell. (c) \(Z_{\text {eff }}\) is usually less than \(Z.\) (d) Electrons in orbitals having \(\ell=1\) penetrate better than those with \(\ell=2.\) (e) \(\mathrm{Z}_{\text {eff }}\) for the orbitals of the elements \(\mathrm{Na}(3 s)\) \(\mathrm{Mg}(3 s), \mathrm{Al}(3 p), \mathrm{P}(3 p),\) and \(\mathrm{S}(3 p)\) are in the order \(Z_{\text {eff }}(\mathrm{Na})<\mathrm{Z}_{\text {eff }}(\mathrm{Mg})>\mathrm{Z}_{\text {eff }}(\mathrm{Al})<\mathrm{Z}_{\text {eff }}(\mathrm{P})>\mathrm{Z}_{\text {eff }}(\mathrm{S}).\)

Short answer

The correct answers are: (a) False, (b) False, (c) True, (d) True, (e) False. The explanation for each statement relies on understanding how the effective nuclear charge and electron shielding work in multi-electron atoms.

Step-by-step solution

Evaluate Statement (a)

Statement (a) says that electrons in a \(p\) orbital are more effective in shielding other electrons from the nuclear charge than electrons in the \(s\) orbital. However, this is actually false. Electrons in the \(s\) orbital are closer to the nucleus and hence more effective at shielding than those in the \(p\) orbital.

Evaluate Statement (b)

Statement (b) claims that the effective nuclear charge for an electron in an \(s\) orbital is lower than that for an electron in a \(p\) orbital in the same shell. This is false. Electrons in an \(s\) orbital experience a higher effective nuclear charge than those in a \(p\) orbital in the same shell because \(s\) electrons are closer to the nucleus.

Evaluate Statement (c)

Statement (c) states that \(Z_{\text {eff }}\) is usually less than \(Z.\) This is true. The effective nuclear charge is less than the actual nuclear charge because of shielding by other electrons in the atom.

Evaluate Statement (d)

Statement (d) says that electrons in orbitals having \(\ell=1\) penetrate better than those with \(\ell=2.\) This is true. The value of \(\ell\), the azimuthal quantum number, reflects the shape of the orbital; \(\ell=1\) represents \(p\) orbitals and \(\ell=2\) represents \(d\) orbitals. \(p\) orbitals penetrate closer to the nucleus compared to \(d\) orbitals, due to their shapes and node structures.

Evaluate Statement (e)

Statement (e) provides a specific order for the effective nuclear charge for orbitals of different elements. This order implies that \(Z_{\text {eff }}(\mathrm{Na})<\mathrm{Z}_{\text {eff }}(\mathrm{Mg})>\mathrm{Z}_{\text {eff }}(\mathrm{Al})<\mathrm{Z}_{\text {eff }}(\mathrm{P})>\mathrm{Z}_{\text {eff }}(\mathrm{S}).\) However, the correct order is \(Z_{\text {eff }}(\mathrm{Na})<\mathrm{Z}_{\text {eff }}(\mathrm{Mg})<\mathrm{Z}_{\text {eff }}(\mathrm{Al})<\mathrm{Z}_{\text {eff }}(\mathrm{P})<\mathrm{Z}_{\text {eff }}(\mathrm{S})\), so statement (e) is false.

Key concepts

Orbital Shielding

In an atom, electrons are arranged in different orbitals, which are regions around the nucleus where there is a high probability of finding an electron. Electrons that are closer to the nucleus can partially block or "shield" the nuclear charge felt by electrons that are further away. This shielding effect is important because it helps explain why electrons in outer shells experience a lower effective nuclear charge compared to the actual charge of the nucleus.

- Electrons in an s orbital, which are closer to the nucleus, shield the nuclear charge more effectively than electrons in p or d orbitals.
- This means that s electrons can better obscure the full charge of the nucleus from other electrons, reducing the effective nuclear charge those outer electrons experience.

Understanding shielding is crucial for grasping how electrons in larger atoms feel less pull from the nucleus due to the layers of inner electron shielding.

Electronic Penetration

Electronic penetration describes how close an electron in a particular orbital can get to the nucleus. The closer an electron can get, the more strongly it is attracted to the nucleus, which affects the effective nuclear charge it experiences.

- Electrons in s orbitals are closer to the nucleus and thus "penetrate" more compared to electrons in p orbitals.
- This means s orbitals have a greater penetration ability than p orbitals which affects the effectiveness of shielding and the effective nuclear charge an electron experiences in higher shells.

Penetration is significant in explaining why electrons in different orbital types (s, p, d, and f) have different energies even within the same principal energy level.

Quantum Numbers

Quantum numbers are essential for understanding the behavior and orientation of electrons in atoms. They describe the size, shape, and energy of electron orbitals.

There are four types of quantum numbers:

• Principal Quantum Number (n): Indicates the energy level the electron is in. Higher n means electrons are further from the nucleus.
• Azimuthal Quantum Number (l): Defines the shape of the orbital. Values range from 0 to n-1, where 0 is for s, 1 for p, 2 for d, and so on.
• Magnetic Quantum Number (m): Determines the orientation in space of the orbital.
• Spin Quantum Number (ms): Specifies the spin direction of the electron, with possible values of +1/2 or -1/2.

Understanding quantum numbers helps us predict the properties of atoms, how electrons fill available orbitals, and how atoms will interact with each other.

Periodic Trends

Periodic trends explain the patterns observed in the properties of elements across different periods and groups of the Periodic Table. These trends are largely influenced by effective nuclear charge, atomic radius, ionization energy, and electron shielding.

Major Trends:

• Atomic Size: Generally decreases across a period due to increased nuclear charge pulling electrons closer, and increases down a group as more electron shells are added.
• Ionization Energy: The energy required to remove an electron from an atom. It increases across a period due to stronger effective nuclear charge and decreases down a group.
• Electronegativity: A measure of an atom's ability to attract bonding electrons, increasing across a period and decreasing down a group.

Understanding these periodic trends allows us to predict the chemical behavior of elements and their compounds, providing a roadmap for their reactivity and interactions.