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The magnetic quantum number (ml) is one of four quantum numbers in atomic physics and quantum chemistry that characterise an electron’s unique quantum state (the others being the primary, azimuthal, and spin). The magnetic quantum number is used to compute the azimuthal component of an orbital’s orientation in space and to differentiate the orbitals accessible inside a subshell. Values of l specify electrons in a certain subshell (such as s, p, d, or f) (0, 1, 2, or 3). The value of ml can be anything between -l and +l, including zero. As a result, the s, p, d, and f subshells each have 1, 3, 5, and 7 orbitals, with m values ranging from 0 to 1, 2, 3, respectively. The periodic table is made up of these orbitals, each of which may hold up to two electrons (with opposing spins).
Magnetic Quantum Numbers
The direction of the angular momentum vector is roughly referred to by the quantum number m. Because all spherical harmonics corresponding to various arbitrary values of m are identical in the absence of a magnetic field, the magnetic quantum number m only influences the electron’s energy if it is in one. The magnetic quantum number, as the name implies, defines the energy shift of an atomic orbital owing to an external magnetic field (the Zeeman effect). The real magnetic dipole moment of an electron in an atomic orbital, on the other hand, is determined not only by the electron angular momentum, but also by the electron spin, which is given in the spin quantum number.
Because each electron has a magnetic moment in a magnetic field, it is subjected to a torque that causes the vector L to become parallel to the field, a phenomenon known as Larmor precession.
Energy State
Bound quantum mechanical systems or particles may only take on discrete quantities of energy, called energy levels. Unlike classical particles, which can have any energy. The phrase usually refers to the energy levels of electrons in atoms, ions, or molecules bound by the nucleus’ electric field, but it may also apply to nuclei’s energy levels or vibrational or rotational energy levels. Quantized the energy spectrum of a system having discrete energy levels.
An electron shell, or primary energy level, is the orbit of one or more electrons around an atom’s nucleus. The 1 shell is closest to the nucleus, followed by the 2 shell (or “L shell”), the 3 shell (or “M shell”), and so on. The shells are either labelled with the major quantum numbers (n = 1, 2, 3, 4,…) or with letters from the X-ray notation (K, L, M, N…).
Each shell can only hold so many electrons: The first shell may store two electrons, the second eight (2 + 6) electrons, the third 18 (2 + 6 + 10) electrons, and so on. The nth shell may theoretically store 2n2 electrons. Because electrons are electrically attracted to the nucleus, they will only occupy outer shells if the inner shells are already entirely occupied. However, atoms can have two or three incomplete outer shells. (See Madelung rule.) See electron configuration for why electrons are in these shells.
Bound electron states have negative potential energy if the potential energy is set to zero at an infinite distance from the atomic nucleus or molecule.
The ground state is the lowest possible energy level for an atom, ion, or molecule. It is considered to be thrilled if it has a greater energy level than the ground state. Degenerate energy levels have several detectable quantum mechanical states.
Shapes of Orbitals
An orbital is an area of space surrounding the nucleus where the chances of finding an electron of a certain energy are greatest. The orbital form is determined by the geometry of this area (electron cloud). The forms of orbitals are determined by plotting angular wave functions or square angular wave functions (probability functions). Only a small difference exists between these two graphs. Let’s have a look at the distinct forms.
S-Orbitals Have A Certain Shape
When l = 0, the value of m is 0, indicating that there is only one potential orientation for s-orbitals. This indicates that at a certain distance from the nucleus, the likelihood of discovering an electron is the same in all directions. As a result, it should have a spherical form. As a result, all s- orbitals around the nucleus are non-directional and spherically symmetrical.
p-Orbitals’ Shape
There are three values of m for p-subshell l = 1, namely -1, 0, and +1. It indicates that there are three potential orientations for p orbitals. These three p-orbitals have the same energy (degenerate state), but their orientations are different. Each p-orbital is made up of two lobes that are symmetrical around a single axis. The lobes are indicated as 2px, 2py, and 2pz depending on their orientation, as they are symmetrical around the X,Y, and Z axes, respectively.
D-Orbitals Have A Certain Shape
There are five values of m for d-subshell, l = 2, namely -2, -1, 0, 1, 2. It indicates that d- orbitals can have up to five different orientations. Dxy, dyz, dzx, dx2-y2, and dz2 are used to express these; for example, 3dxy, 3dyz, 3dzx, 3dx2-y2, and 3dz2. The dxy, dyz, and dzx orbitals all have the same form, a clover leaf, but they are located in the XY, YZ, and ZX- planes, respectively. The dz2 orbital has a dumb – bell shape with a doughnut-shaped electron cloud in the centre and is symmetrical about the Z-axis. The leaves of the dx2-y2 orbital are likewise clovar leaf shaped, but they are oriented along the X and Y axes.
Conclusion
The number of orbitals and their orientation inside a subshell are determined by the magnetic quantum number ml. As a result, the orbital angular momentum quantum number l determines its value. ml is an interval ranging from –l to +l, so it can be zero, a negative integer, or a positive integer given a certain l.
