Yes, the 5d orbital is indeed possible.
Atomic orbitals describe the probable location of electrons around an atom's nucleus. Their existence and characteristics are governed by a set of quantum numbers, which dictate their size, shape, and orientation in space.
Understanding 5d Orbitals
The '5' in 5d indicates the principal quantum number (n = 5), which relates to the electron shell and energy level. The 'd' indicates the type of subshell, corresponding to an azimuthal quantum number (l = 2).
For an orbital to exist, the azimuthal quantum number (l) must always be less than the principal quantum number (n). In the case of a 5d orbital:
- Principal Quantum Number (n): 5
- Azimuthal Quantum Number (l): 2 (for d orbitals)
Since 2 is less than 5, the 5d orbital is a valid and possible electron orbital.
The Five 5d Orbitals
For any 'd' subshell (where l = 2), there are always five individual orbitals. These are differentiated by their magnetic quantum number ($m_l$), which can range from -l to +l. For l=2, $m_l$ can be -2, -1, 0, 1, or 2, resulting in five distinct orbitals.
These five 5d orbitals are typically labelled based on their spatial orientation and shape:
- 5d$_{xy}$
- 5d$_{xz}$
- 5d$_{yz}$
- 5d$_{x^2-y^2}$
- 5d$_{z^2}$
Four of these orbitals (5d${xy}$, 5d${xz}$, 5d${yz}$, and 5d${x^2-y^2}$) share a similar four-lobed shape, but they are aligned differently along the x, y, and z axes. The fifth orbital, 5d$_{z^2}$, has a distinct shape, often described as two lobes along the z-axis with a donut-like ring in the xy-plane.
Quantum Numbers and Orbital Possibility
The possibility of atomic orbitals is directly derived from the rules of quantum mechanics. Here's a brief overview:
| Quantum Number | Symbol | Description | Range | Relevance to 5d Orbital |
|---|---|---|---|---|
| Principal | n | Defines the energy level and shell number. Higher 'n' means higher energy and larger size. | 1, 2, 3... (positive integers) | For 5d, n = 5 |
| Azimuthal (Angular Momentum) | l | Defines the shape of the orbital and subshell (s, p, d, f). | 0 to n-1 | For 5d, l = 2 (d-orbital) |
| Magnetic | $m_l$ | Defines the orientation of the orbital in space. | -l to +l (including 0) | For 5d, $m_l$ = -2, -1, 0, 1, 2 (5 orientations) |
| Spin | $m_s$ | Describes the intrinsic angular momentum (spin) of an electron. | +1/2 or -1/2 | Not directly relevant to orbital existence, but to electron filling |
Since n=5 allows for l values up to 4 (0, 1, 2, 3, 4), and l=2 (for 'd' orbitals) falls within this range, the 5d orbital is perfectly valid and observable in multi-electron atoms.
Role in Chemistry
5d orbitals become occupied by electrons in various elements, particularly in the later periods of the periodic table. They play a crucial role in:
- Transition Metals: Elements in the 5th and 6th periods (e.g., Yttrium, Zirconium, Hafnium, Tantalum, Tungsten, Gold, Mercury) utilize 5d orbitals in their ground state electron configurations, which significantly influences their chemical properties, variable oxidation states, and ability to form complex ions.
- Lanthanides and Actinides: While primarily filling f-orbitals, some of these elements also have electrons in their 5d orbitals.
- Chemical Bonding: The shape and orientation of 5d orbitals are fundamental to understanding molecular geometry and bonding in compounds involving these elements.
