What are quantum numbers? What permitted values can these have? Explain their significance.
Answers
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A quantum number is a value that is used when describing the energy levels available to atoms and molecules. An electron in an atom or ion has four quantum numbers to describe its state and yield solutions to the Schrödinger wave equation for the hydrogen atom.
The principal quantum number is an integer that is the number of the electron's shell. The value is 1 or higher (never 0 or negative).
The angular momentum quantum number is an integer that is the value of the electron's orbital (e.g., s=0, p=1). ℓ is greater than or equal to zero and less than or equal to n-1.
The magnetic quantum number is the orientation of the orbital with integer values ranging from -ℓ to ℓ. So, for the p orbital, where ℓ=1, m could have values of -1, 0, 1.
The spin quantum number is a half-integer value that is either -1/2 (called "spin down") or 1/2 (called "spin up").
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# BeBrainly
Answer:
The set of numbers used to describe the position and energy of the electron in an atom are called quantum numbers.
Explanation:
Each electron in an atom is described by four different quantum numbers. The first three (n, l,
ml) specify the particular orbital of interest, and the fourth (ms) specifies how many electrons can
occupy that orbital.
1. Principal Quantum Number (n): n = 1, 2, 3, …, 8 .
Specifies the energy of an electron and the size of the orbital (the distance from the nucleus of
the peak in a radial probability distribution plot). All orbitals that have the same value of n
are said to be in the same shell (level). For a hydrogen atom with n=1, the electron is in its
ground state; if the electron is in the n=2 orbital, it is in an excited state. The total number of
orbitals for a given n value is n2
2. Angular Momentum (Secondary, Azimunthal) Quantum Number (l): l = 0, ..., n-1.
Specifies the shape of an orbital with a particular principal quantum number. The secondary
quantum number divides the shells into smaller groups of orbitals called subshells (sublevels).
Usually, a letter code is used to identify l to avoid confusion with n:
l 0 1 2 3 4 5 . . .
Letter s p d f g h . . .
The subshell with n=2 and l=1 is the 2p subshell; if n=3 and l=0, it is the 3s subshell, and so
on.
The value of l also has a slight effect on the energy of the subshell; the energy of the
subshell increases with l (s < p < d < f).
3. Magnetic Quantum Number (ml): ml= -l, ..., 0, ..., +l.
Specifies the orientation in space of an orbital of a given energy (n) and shape (l).
This number divides the subshell into individual orbitals which hold the electrons; there are 2l+1
orbitals in each subshell. Thus the s subshell has only one orbital, the p subshell has three
orbitals, and so on.
Spin Quantum Number (ms): ms = +½ or -½.
Specifies the orientation of the spin axis of an electron. An electron can spin in only one of
two directions (sometimes called up and down)