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In quantum mechanics, the principal quantum number (symbolized n) is one of four quantum numbers assigned to each electron in an atom to describe that electron's state. Its values are natural numbers (from one) making it a discrete variable . Apart from the principal quantum number, the other quantum numbers for bound electrons are the ...
Quantum numbers are closely related to eigenvalues of observables. When the corresponding observable commutes with the Hamiltonian, the quantum number is said to be "good", and acts as a constant of motion in the quantum dynamics. To fully specify the state of the electron in a hydrogen atom, four quantum numbers are needed.
Quantum mechanics is a fundamental theory in physics that describes the behavior of nature at and below the scale of atoms. [2] : 1.1 It is the foundation of all quantum physics, which includes quantum chemistry, quantum field theory, quantum technology, and quantum information science . Quantum mechanics can describe many systems that ...
The first dictates that no two electrons in an atom may have the same set of values of quantum numbers (this is the Pauli exclusion principle). These quantum numbers include the three that define orbitals, as well as the spin magnetic quantum number m s. Thus, two electrons may occupy a single orbital, so long as they have different values of m s.
e. Quantum mechanics is the study of matter and its interactions with energy on the scale of atomic and subatomic particles. By contrast, classical physics explains matter and energy only on a scale familiar to human experience, including the behavior of astronomical bodies such as the moon. Classical physics is still used in much of modern ...
If the group is of the [d] or [f], type, an amount of 1.00 for each electron "closer" to the nucleus than the group. This includes both i) electrons with a smaller principal quantum number than n and ii) electrons with principal quantum number n and a smaller azimuthal quantum number l. In tabular form, the rules are summarized as:
In the case of electrons in atoms, the exclusion principle can be stated as follows: in a poly-electron atom it is impossible for any two electrons to have the same two values of all four of their quantum numbers, which are: n, the principal quantum number; ℓ, the azimuthal quantum number; m ℓ, the magnetic quantum number; and m s, the spin ...
The quantum numbers corresponding to these operators are , , (always 1/2 for an electron) and respectively. The energy levels in the hydrogen atom depend only on the principal quantum number n . For a given n , all the states corresponding to ℓ = 0 , … , n − 1 {\displaystyle \ell =0,\ldots ,n-1} have the same energy and are degenerate.