Azimuthal Quantum Number

The azimuthal quantum number is a quantum number that characterises the form of an atomic orbital and defines its orbital angular momentum. The azimuthal quantum number is the second in a series of quantum numbers that describe an electron’s distinct quantum state (the others being the principal quantum number, the magnetic quantum number, and the spin quantum number). It’s also known as the quantum number of orbital angular momentum. Arnold Sommerfeld proposed the azimuthal quantum number, which was derived from the Bohr model of the atom. The Bohr model was created by combining the Rutherford atomic model with spectroscopic examination of the atom. 

Azimuthal Quantum Number

• The geometry of an orbital is described by the azimuthal quantum number (or orbital angular momentum quantum number). Its value equals the total number of angular nodes in the orbital and is symbolised by the letter
• An s,p,d and f subshell with varying forms can be represented by a value of the azimuthal quantum number. The value of the primary quantum number determines (and limits) this value, i.e. the azimuthal quantum number spans between 0 and 1. n-1.
• Arnold Sommerfeld proposed the azimuthal quantum number, which is an enlarged version of the Bohr model of the atom. He claims that, in addition to the circular orbits described by Bohr, elliptical orbits exist, implying that each shell is made up of several subshells.
• The azimuthal quantum number is the quantum number for an atomic orbital that describes the orbital form as well as the momentum of its orbital angle. It is the second set of quantum numbers that describes an electron’s unique quantum state. It is designated by land aids in identifying the ellipticity of the subshells. It’s also known as an orbital angular momentum quantum number, an orbital quantum number, or a second quantum number.

The azimuthal quantum number also provides us with other information, such as:

• The number of subshells found in an atom’s primary shell.
• The electrons in the subshell have an angular momentum.
• Subshell energies, or relative energies.
• The shape of the main shell’s different subshells.

The azimuthal quantum number, l is the quantum number that corresponds to an atomic electron’s angular momentum. It’s also known as the second quantum number or the angular momentum quantum number. The form of the electron’s orbital is determined by the angular momentum quantum number.

Azimuthal Quantum Number Formula

Sommerfeld introduced the azimuthal quantum number in his atomic structure. As a result, Sommerfeld calculates the angular momentum of an electron as it moves elliptically around an atom’s nucleus. As a result, the azimuthal or angular momentum quantum number determines the general geometric shapes of an electron cloud or orbitals.

For a given value of n, the allowed values of l range from 0 to 1.(n-1)As a result, the magnetic quantum numbers l=0,1,2,3,….(n-1)are generated. However, the total number of different lvalues equals n. l=0or 1s-orbital when n=1However, 2p-orbitals forn=2, l=0,1 or 2s. When n=3andl=0, the orbitals are l,2 or 3s,3p and 3d orbitals. 

Azimuthal Quantum Number Properties

• The form of an orbital is determined by the azimuthal (or orbital angular momentum) quantum number. Its value is always equal to the total number of angular nodes contained in the orbital, and it is symbolised by the symbol l.
• An s,p,d and f subshell with a different form is designated by a value of the azimuthal quantum number. The value of l, or the Azimuthal Quantum Number, is determined by the primary quantum number’s value.
• Apart from the main quantum number (n), spectroscopic notation, magnetic quantum number (m), and spin quantum number (s), the azimuthal quantum number is another set of quantum numbers that define an electron’s unique quantum state. It’s described as the quantum number attached with an atomic electron’s angular momentum.
• The orbital angular momentum quantum number, also known as the orbital quantum number or second quantum number, is denoted by the letter l This value controls the orbital angular momentum as well as the shape of the orbital. A p orbital coupled with an azimuthal quantum number of 1 is an example of the angular quantum momentum number.

Conclusion

The Azimuthal quantum number is a quantum number that characterises the form of an atomic orbital and defines its orbital angular momentum. The Bohr model was created by combining the Rutherford atomic model with spectroscopic examination of the atom. Sommerfeld introduced the azimuthal quantum number in his atomic structure. The value of l, or the Azimuthal Quantum Number, is determined by the primary quantum number’s value. The azimuthal quantum number is the quantum number for an atomic orbital that describes the orbital form as well as the momentum of its orbital angle. The form of the electron’s orbital is determined by the angular momentum quantum number.