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The route and movement of an electron within an atom may be described using quantum numbers. The Schrodinger equation must be satisfied when the quantum numbers of all the electrons in a particular atom are combined together. The collection of numbers used to characterise the location and energy of an electron in an atom is known as quantum numbers. Quantum numbers are divided into four categories: primary, azimuthal, magnetic, and spin. Quantum numbers are the values of the preserved quantities in a quantum system. The Schrodinger wave equation for hydrogen atoms is solved using electronic quantum numbers (quantum numbers characterising electrons).
Types Of Quantum Numbers
To properly express all of the characteristics of a specific electron in an atom, four quantum numbers can be used:
- Principal quantum number
- Orbital angular momentum quantum number (or azimuthal quantum number).
- Magnetic quantum number
- The electron spin quantum number
The principal quantum numbers are represented by the symbol ‘n.’ They represent the main electron shell of an atom. A bigger value of the primary quantum number denotes a greater distance between the nucleus and the electrons since it indicates the most likely distance between the nucleus and the electrons (which, in turn, implies a greater atomic size).
The form of an orbital is described by the azimuthal quantum number (or orbital angular momentum). Its value equals the total number of angular nodes in the orbital and is symbolised by the letter ‘l.’
The total number of orbitals in a subshell, as well as their orientation, is determined by the magnetic quantum number. The symbol ‘ml’ is used to symbolise it. This quantity indicates the orbital angular momentum projected along a specified axis.
The electron spin quantum number is unaffected by the values of n, l, and ml. The direction in which the electron spins is indicated by the value of this number, represented by the symbol ms.
Schrodinger Wave Equation
A quantum-mechanical system’s wave function is governed by the Schrödinger equation, which is a linear partial differential equation: 1–2 It’s a crucial finding in quantum physics, and its discovery marked a watershed moment in the field’s evolution. The equation is named after Erwin Schrödinger, who proposed it in 1925 and published it in 1926, laying the groundwork for his Nobel Prize-winning work in Physics in 1933.
The Schrödinger equation is the quantum analogue of Newton’s second law in classical mechanics in terms of concept. Newton’s second law gives a mathematical prediction about the route a particular physical system will follow over time given a set of known beginning circumstances. The Schrödinger equation describes the development of a wave function over time, which is the quantum-mechanical characterisation of a physically isolated system. Because the time-evolution operator must be unitary, the quantum Hamiltonian must be created by the exponential of a self-adjoint operator.
Quantum Numbers and Atomic Orbitals
n = 1, 2, 3,…,
Describes an electron’s energy and orbital size (the distance from the nucleus of the peak in a radial probability distribution plot). All orbitals with the same n value are in the same shell (level). An electron in the n=1 orbital of a hydrogen atom is in the ground state; an electron in the n=2 orbital is excited. A given n value has n2 orbitals.
The Angular Momentum Quantum Number (l) is 0 to n-1.
Describes an orbital’s form for a certain primary quantum number. The secondary quantum number separates the shells into subshells (sublevels). To distinguish l from n, a letter code is usually used:
l 0 1 2 3 4 5 …
Letter s p d f g h …
The 2p subshell has n=2 and l=1, 3s has n=3 and l=0, and so on. The subshell’s energy grows with l (s p d f).
ml = -l,…, 0,…, +l.
Orients an orbital of a given energy (n) and shape in space (l). Each subshell has 2l+1 orbitals that store electrons. So the s subshell has one orbital, the p subshell has three, etc.
ms = +12 or -12.
Orients an electron’s spin axis. An electron can only spin in one way (sometimes called up and down).
The Pauli exclusion principle asserts that no two electrons in the same atom may have the same quantum numbers. This means that two electrons in the same orbital must have opposing spins.
In both directions, an electron’s spin produces a magnetic field. The spins of two electrons in the same orbital must be opposing. These chemicals are diamagnetic, meaning they repel magnets. Unpaired electrons are found in atoms having a lopsided electron spin. Paramagnetic compounds are faintly attracted to magnets.
Conclusion
Quantum numbers are essential because they may be used to figure out an atom’s electron configuration and where its electrons are most likely to be found. Other properties of atoms, such as ionisation energy and atomic radius, are also understood using quantum numbers.
