Question

The correct representation for d orbital is: (a) \((\mathrm{n}-1) \mathrm{d}^{1-9} \mathrm{~ns}^{1}\) (b) \((\mathrm{n}-1) \mathrm{d}^{1-10} \mathrm{~ns}^{1-2}\) (c) \((\mathrm{n}-1) \mathrm{d}^{1-5}\) (d) \((\mathrm{n}-\mathrm{l}) \mathrm{d}^{1-10} \mathrm{~ns}^{2}\)

Short answer

The correct answer is (b) \((n-1)d^{1-10} ns^{1-2}\).

Step-by-step solution

Understand the Question

We need to identify the correct electronic configuration format for d orbitals. The question provides multiple options with different subscripts and superscripts, which indicates the number of electrons in d and s orbitals.

Recall d-Orbital Characteristics

Remember that d orbitals can have a maximum of 10 electrons; the sequence often starts after an s orbital. Typically, the electronic configuration of transition elements uses the (n-1)d orbitals followed by the ns orbital.

Analyze Option (a)

Option (a) represents \((n-1)d^{1-9}\ ns^{1}\). This format allows for 1 to 9 electrons in the d subshell, which is incorrect because the d subshell can contain up to 10 electrons.

Analyze Option (b)

Option (b) represents \((n-1)d^{1-10}\ ns^{1-2}\). This reflects the usual filling of transition metals, where the d subshell can have 1 to 10 electrons, and ns can have 1 to 2 electrons. This is a correct representation.

Analyze Option (c)

Option (c) represents \((n-1)d^{1-5}\). This suggests a maximum of 5 electrons in d orbitals, which is typically not the complete representation for transition metals.

Analyze Option (d)

Option (d) represents \((n-l)d^{1-10}\ ns^{2}\). However, \(n-l\) is not a typical way to refer to d orbitals, making this option incorrect.

Select the Most Appropriate Option

Given the analysis, option (b) \((n-1)d^{1-10}\ ns^{1-2}\) correctly follows the principles of electron configuration for transition elements.

Key concepts

Transition Elements

Transition elements are found in the middle section of the periodic table, specifically in groups 3 to 12. These elements are characterized by their partially filled d orbitals. A defining feature of transition metals is their ability to exhibit multiple oxidation states. This ability is due to the presence of electrons in the d subshell, which can participate in bond formation.

Transition elements usually have high melting and boiling points. They also tend to form colored compounds and have catalytic properties. Unlike the s-block and p-block elements, transition metals often display paramagnetic behavior, which is due to the presence of unpaired electrons in the d orbitals.

Electron Configuration

Electron configuration describes the distribution of electrons among the various atomic orbitals in an atom. This is crucial because it helps to explain and predict chemical properties and behaviors. By following the Aufbau principle, electrons fill orbitals starting with the lowest energy level and move to higher ones as those become filled.

For transition elements, the general electron configuration is typically written as \( ext{[Noble Gas]} (n-1)d^{1-10} ns^{0-2} \). The order of filling does not always follow a straightforward pattern due to the close energy levels between the 3d and 4s orbitals. As a result, 3d orbitals are filled after 4s but are actually written after them in the notation.

d Subshell Filling

The d subshell is a critical component when discussing the electron configuration of transition metals. A d subshell can hold up to 10 electrons. The filling of the d subshell follows Hund's Rule, which states that electrons fill degenerate orbitals singly first before pairing up.

In many cases, electrons initially occupy the d orbital after the s orbital of the same row is partially filled. Once the s orbital is full, electrons are then added to the d subshell until it reaches its maximum capacity of 10 electrons. Knowing this can help in understanding the specific configurations and properties of individual transition elements.

Quantum Numbers

Quantum numbers are critical in determining the electron configuration and, consequently, the chemical properties of an element. Each electron in an atom is described by four quantum numbers: the principal quantum number (n), the azimuthal quantum number (l), the magnetic quantum number (m_l), and the spin quantum number (m_s).

- The principal quantum number (n) determines the energy level of an electron and its average distance from the nucleus.- The azimuthal quantum number (l) defines the shape of the orbital. For d orbitals, l equals 2.- The magnetic quantum number (m_l) indicates the orientation of the orbital in space, whereas, for d orbitals, m_l can be -2, -1, 0, 1, or 2.- The spin quantum number (m_s) illustrates the spin orientation of an electron; it can either be \(+\) or \(-\).

These numbers not only help us understand electronic configurations but also provide insights into the chemical behavior and reactivity of various elements.