What is the Azimuthal quantum number (pardon if the spelling is wrong) ?

Answer 1

The Azimuthal quantum number (or orbital angular momentum quantum number) l is a quantum number for an atomic orbital which determines its orbital angular momentum. Their wavefunctions take the form of spherical harmonics, and so are described by Legendre polynomials. ...

The azimuthal quantum number was carried over from the Bohr model of the atom. The Bohr model was derived as was all of quantum theory from spectroscopic analysis of the atom in combination with the Rutherford atom. This is due to the fact that each atom of each element produces a unique quantum pattern of spectral lines when light from each different kind of element is passed through a prism. Whenever an electron drops to a lower energy level or lower n-orbital, it emits a photon which shows up on the spectrum according to its wavelength. The first orbital n of the Bohr atom, called the K-shell at times, is in the ultraviolet spectrum and was therefore discovered after the Balmer series which is in the visible light spectrum. Bohr argued that the angular momentum in any orbit n was nKh, where h is Planck's constant and K is some multiplying factor, the same for all the orbits, which was later determined to be 1/2π. The lowest quantum level therefore had an angular momentum of zero. Because orbits were one-dimensionalized in mathematics for simplicity to oscillating charges, this was originally described as a "pendulum" orbit because it was linear. However in three-dimensions the orbit becomes spherical without any nodes crossing the nucleus as in the case of a vibrating string on a musical instrument that were to oscillate in one large circle (similar to a jump rope) thereby creating a standing wave that did not intersect with the nucleus.

The Azimuthal quantum number (or orbital/total angular momentum quantum number) symbolized as l (lower-case L) is a quantum number for an atomic orbital which determines its orbital angular momentum. The azimuthal quantum number is the second of a set of quantum numbers (the principal quantum number, following Spectroscopic notation, the azimuthal quantum number, the magnetic quantum number, and the spin quantum number) which describe the unique quantum state of an electron and is designated by the letter l.

There are a set of quantum numbers associated with the energy states of the atom. The four quantum numbers n, l, ml, and s specify the complete and unique quantum state of a single electron in an atom called its wavefunction or orbital. The wavefunction of the Schrödinger wave equation reduces to the three equations that when solved lead to the first three quantum numbers. Therefore, the equations for the first three quantum numbers are all interrelated. The azimuthal quantum number arose in the solution of the polar part of the wave equation as shown below.

An atomic electron's angular momentum, L, which is related to its quantum number is described by the following equation:


where is the reduced Planck's constant, also called Dirac's constant, is the orbital angular momentum operator and is the wavefunction of the electron. While many introductory text books on quantum mechanics will refer to L by itself, L has no real meaning except in its use as the angular momentum operator. When refering to angular momentum, it is best to simply use the the quantum number .

The energy of any wave is the frequency multiplied by Planck's constant. This causes the wave to display particle-like packets of energy called quanta. To show each of the quantum numbers in the quantum state, the formulae for each quantum number include Planck's reduced constant which only allows particular or discrete or quantized energy levels.

This behavior manifests itself as the "shape" of the orbital.


The atomic orbital wavefunctions of a hydrogen atom. The principal quantum number is at the right of each row and the azimuthal quantum number is denoted by letter at top of each column.Electron shells have distinctive shapes denoted by letters. In the illustration, the letters s, p, and d describe the shape of the atomic orbital.

...all the best.

Answer 2

Azimuthal Quantum Number

Answer 3

The Azimuthal quantum number (or orbital/total angular momentum quantum number) symbolized as l (lower-case L) is a quantum number for an atomic orbital which determines its orbital angular momentum. The azimuthal quantum number is the second of a set of quantum numbers (the principal quantum number, following Spectroscopic notation, the azimuthal quantum number, the magnetic quantum number, and the spin quantum number) which describe the unique quantum state of an electron and is designated by the letter l.

Answer 4

L=2

Answer 5

RE:
What is the Azimuthal quantum number (pardon if the spelling is wrong) ?

Answer 6

The Azimuthal quantum number (or orbital/total angular momentum quantum number) symbolized as l (lower-case L) is a quantum number for an atomic orbital which determines its orbital angular momentum. The azimuthal quantum number is the second of a set of quantum numbers (the principal quantum number, following Spectroscopic notation, the azimuthal quantum number, the magnetic quantum number, and the spin quantum number) which describe the unique quantum state of an electron and is designated by the letter l.............
got it ?......i haven't :-)

Answer 7

azimuthal quantum number which is also known as orbital quantum number is used to represent the angular momentum of the electron in an atom it is represented by the letter l

Answer 8

The Azimuthal quantum number (or orbital/total angular momentum quantum number) symbolized as l (lower-case L) is a quantum number for an atomic orbital which determines its orbital angular momentum. The azimuthal quantum number is the second of a set of quantum numbers (the principal quantum number, following Spectroscopic notation, the azimuthal quantum number, the magnetic quantum number, and the spin quantum number) which describe the unique quantum state of an electron and is designated by the letter l.

There are a set of quantum numbers associated with the energy states of the atom. The four quantum numbers n, l, ml, and s specify the complete and unique quantum state of a single electron in an atom called its wavefunction or orbital. The wavefunction of the Schrödinger wave equation reduces to the three equations that when solved lead to the first three quantum numbers. Therefore, the equations for the first three quantum numbers are all interrelated. The azimuthal quantum number arose in the solution of the polar part of the wave equation as shown below.

An atomic electron's angular momentum, L, which is related to its quantum number is described by the following equation:


where is the reduced Planck's constant, also called Dirac's constant, is the orbital angular momentum operator and is the wavefunction of the electron. While many introductory text books on quantum mechanics will refer to L by itself, L has no real meaning except in its use as the angular momentum operator. When refering to angular momentum, it is best to simply use the the quantum number .

The energy of any wave is the frequency multiplied by Planck's constant. This causes the wave to display particle-like packets of energy called quanta. To show each of the quantum numbers in the quantum state, the formulae for each quantum number include Planck's reduced constant which only allows particular or discrete or quantized energy levels.

This behavior manifests itself as the "shape" of the orbital.

Electron shells have distinctive shapes denoted by letters. In the illustration, the letters s, p, and d describe the shape of the atomic orbital.

Their wavefunctions take the form of spherical harmonics, and so are described by Legendre polynomials. The various orbitals relating to different values of l are sometimes called sub-shells, and (mainly for historical reasons) are referred to by letters, as follows:

l Letter Max electrons Shape Name
0 s 2 sphere sharp
1 p 6 two dumbbells principal
2 d 10 four dumbbells diffuse
3 f 14 eight dumbbells fundamental
4 g 18
5 h 22
6 i 26

A mnemonic for the order of the "shells" is some poor dumb fool. Another mnemonic for the order of the "shells" is silly professors dance funny. The letters after the F subshell just follow F in alphabetical order.

Each of the different angular momentum states can take 2(2l+1) electrons. This is because the third quantum number ml (which can be thought of loosely as the quantised projection of the angular momentum vector on the z-axis) runs from −l to l in integer units, and so there are 2l+1 possible states. Each distinct nlml orbital can be occupied by two electrons with opposing spins (given by the quantum number ms), giving 2(2l+1) electrons overall. Orbitals with higher l than given in the table are perfectly permissible, but these values cover all atoms so far discovered.

For a given value of the principal quantum number, n, the possible values of l range from 0 to n−1; therefore, the n=1 shell only possesses an s subshell and can only take 2 electrons, the n=2 shell possesses an s and a p subshell and can take 8 electrons overall, the n=3 shell possesses s, p and d subshells and has a maximum of 18 electrons, and so on (generally speaking, the maximum number of electrons in the nth energy level is 2n2).

The angular momentum quantum number, l, governs the ellipticity of the probability cloud and the number of planar nodes going through the nucleus. A planar node can be described in an electromagnetic wave as the midpoint between crest and trough which has zero magnitude. A sine wave has a portion with a positive magnitude, a portion with a negative magnitude, and a node, which has zero magnitude. In an s orbital, no nodes go through the nucleus, therefore the corresponding azimuthal quantum number l takes the value of zero. In a p orbital, one node traverses the nucleus and therefore l has the value 1.

Depending on the value of n, the principal quantum number, there is an angular momentum quantum number l and the following series:

n = 1, l = 0, Lyman series (ultraviolet)
n = 2, l = ħ, Balmer series (visible) Wavelength vary from 400 to 700 nm
n = 3, l = 2ħ, Ritz-Paschen series (short wave infrared)
n = 4, l = 3ħ, Pfund series (long wave infrared)

[edit] Addition of quantized angular momenta
Given a quantized total angular momentum which is the sum of two individual quantized angular momenta and ,


the quantum number j associated with its magnitude can range from | l1 − l2 | to l1 + l2 in integer steps where l1 and l2 are quantum numbers corresponding to the magnitudes of the individual angular momenta.


[edit] List of angular momentum quantum numbers
Intrinsic (or spin) angular momentum quantum number, or simply spin quantum number
orbital angular momentum quantum number
magnetic quantum number, related to the orbital momentum quantum number
total angular momentum quantum number

[edit] History
The azimuthal quantum number was carried over from the Bohr model of the atom. The Bohr model was derived as was all of quantum theory from spectroscopic analysis of the atom in combination with the Rutherford atom. This is due to the fact that each atom of each element produces a unique quantum pattern of spectral lines when light from each different kind of element is passed through a prism. Whenever an electron drops to a lower energy level or lower n-orbital, it emits a photon which shows up on the spectrum according to its wavelength. The first orbital n of the Bohr atom, called the K-shell at times, is in the ultraviolet spectrum and was therefore discovered after the Balmer series which is in the visible light spectrum. Bohr argued that the angular momentum in any orbit n was nKh, where h is Planck's constant and K is some multiplying factor, the same for all the orbits, which was later determined to be 1/2π. The lowest quantum level therefore had an angular momentum of zero. Because orbits were one-dimensionalized in mathematics for simplicity to oscillating charges, this was originally described as a "pendulum" orbit because it was linear. However in three-dimensions the orbit becomes spherical without any nodes crossing the nucleus as in the case of a vibrating string on a musical instrument that were to oscillate in one large circle (similar to a jump rope) thereby creating a standing wave that did not intersect with the nucleus.