The magnetic quantum number ($m_l$) for a 4d orbital can take on values of -2, -1, 0, 1, and 2.
Understanding Quantum Numbers for a 4d Orbital
To determine the magnetic quantum number ($m_l$) for any orbital, we first need to identify its principal quantum number (n) and azimuthal quantum number (l).
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Principal Quantum Number (n): This number indicates the main energy level of the electron and the size of the orbital. For a 4d orbital, the digit '4' signifies that the principal quantum number n = 4.
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Azimuthal (or Angular Momentum) Quantum Number (l): This number describes the shape of the orbital and the subshell it belongs to. The value of 'l' is determined by the letter designation of the orbital:
- s orbitals: l = 0
- p orbitals: l = 1
- d orbitals: l = 2
- f orbitals: l = 3
Since we are dealing with a 4d orbital, the azimuthal quantum number l = 2.
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Magnetic Quantum Number ($m_l$): This number defines the orientation of the orbital in space. Its values are dependent on 'l' and can range from -l to +l, including zero.
- For an orbital where l = 2 (a d orbital), the possible values for $m_l$ are:
$m_l = -2, -1, 0, 1, 2$
- For an orbital where l = 2 (a d orbital), the possible values for $m_l$ are:
Summary of Quantum Numbers for a 4d Orbital
The following table summarizes the quantum numbers associated with a 4d orbital:
| Quantum Number | Symbol | Value for 4d Orbital | Significance |
|---|---|---|---|
| Principal Quantum Number | n | 4 | Determines the electron shell and energy level. |
| Azimuthal Quantum Number | l | 2 | Specifies the subshell (d) and the shape of the orbital. |
| Magnetic Quantum Number | $m_l$ | -2, -1, 0, 1, 2 | Defines the spatial orientation of the orbital. |
Implications of the Magnetic Quantum Number
Each unique value of $m_l$ corresponds to a distinct orbital within a given subshell. For a 'd' subshell (where l=2), there are 2l + 1 possible $ml$ values, which means there are 2(2) + 1 = 5 d orbitals. These five orbitals have different orientations in three-dimensional space and are commonly denoted as $d{xy}$, $d{xz}$, $d{yz}$, $d{x^2-y^2}$, and $d{z^2}$.
