Quantum Numbers
Important terms and their significance
Size of Orbital: Smaller size means more chance to be found near nucleus. Smaller size means lower energy of a electron in that orbital.
Shape of Orbital: Probability of finding the electron along different directions.
Quantum Numbers: Each orbital is designated by a set of three quantum numbers, each describing a different aspect of the orbital such as size, energy, orientation, etc. The three quantum numbers are namely, Principal Quantum Number(n), Azimuthal Quantum Number (l) and Magnetic Quantum Number ml
Principal Quantum Number
Principal Quantum Number defines the size and to large extent the energy of the orbital. It is a positive integer with the value of n = 1,2,3,…
The energy of Hydrogen atom and Hydrogen-like species (He+, Li2+ …etc.) depends only on the pricnipal quantum number.
Principal Quantum Number identifies the shell represented by letters K, L, M, N, … etc. All the orbitals having a given value of ‘n’ constitute a single shell of the atom.
With increase in the shell number, size of the orbital also increases.
With increase in n, the energy of the orbital will also increase. This is due to requirement of additional energy to pull electron away from the nucleus.
Azimuthal Quantum Number
Also known as subsidiary quantum number and Orbital Angular Momentum, Azimuthal quantum number defines three-dimensional shape of the orbital. It is represented by the letter l. .For a given value of n, l has values from 0 to (n-1).
For example, if n = 3, the possible values of l are 0, 1 and 2.
if n = 5, the possible values of l are 0, 1, 2, 3 and 4 and so on.
Each Azimuthal quantum number lrefers to sub-shell or sub-level of the shell represented by n. The number of sub-shells depends on Principal quantum number and is mathematically equal to n i.e. total numbers of possible values of l = n.
Subshells of given l is represented by following symbols:
Subshell Notations
Magnetic Quantum Number, ‘ml‘
It talks about the spatial orientation of the orbital with respect to standard set of co-ordiante axes. Total number of possible orientations of the orbital depends on the subshell (defined by ‘l‘) value. There are a total of 2l+1 orientations possible for given value of l. For example, if l=3, there are 2×3+1 = 7 possible orientations and hence total number of ml values is 7.
‘ml‘ values varies from –l, –l +1, –l +2, …. -2, -1, 0, +1, +2, …. +l -1, +l
For l = 2, possible values of ‘ml‘ are -2, -1, 0, +1, +2. Thus total number of orbitals for given l=2 is 5.
A quick review of relation between subshell and number of orbitals associated with it
Size of Orbital: Smaller size means more chance to be found near nucleus. Smaller size means lower energy of a electron in that orbital.
Shape of Orbital: Probability of finding the electron along different directions.
Quantum Numbers: Each orbital is designated by a set of three quantum numbers, each describing a different aspect of the orbital such as size, energy, orientation, etc. The three quantum numbers are namely, Principal Quantum Number(n), Azimuthal Quantum Number (l) and Magnetic Quantum Number ml
Principal Quantum Number
Principal Quantum Number defines the size and to large extent the energy of the orbital. It is a positive integer with the value of n = 1,2,3,…
The energy of Hydrogen atom and Hydrogen-like species (He+, Li2+ …etc.) depends only on the pricnipal quantum number.
Principal Quantum Number identifies the shell represented by letters K, L, M, N, … etc. All the orbitals having a given value of ‘n’ constitute a single shell of the atom.
With increase in the shell number, size of the orbital also increases.
| Shell = | K | L | M | N | … | |
|---|---|---|---|---|---|---|
| n = | 1 | 2 | 3 | 4 | … |
Azimuthal Quantum Number
Also known as subsidiary quantum number and Orbital Angular Momentum, Azimuthal quantum number defines three-dimensional shape of the orbital. It is represented by the letter l. .For a given value of n, l has values from 0 to (n-1).
For example, if n = 3, the possible values of l are 0, 1 and 2.
if n = 5, the possible values of l are 0, 1, 2, 3 and 4 and so on.
Each Azimuthal quantum number lrefers to sub-shell or sub-level of the shell represented by n. The number of sub-shells depends on Principal quantum number and is mathematically equal to n i.e. total numbers of possible values of l = n.
Subshells of given l is represented by following symbols:
| Value for l : | 0 | 1 | 2 | 3 | 4 | 5 | … | |
|---|---|---|---|---|---|---|---|---|
| Notation for sub shell : | s | p | d | f | g | h | … |
Magnetic Quantum Number, ‘ml‘
It talks about the spatial orientation of the orbital with respect to standard set of co-ordiante axes. Total number of possible orientations of the orbital depends on the subshell (defined by ‘l‘) value. There are a total of 2l+1 orientations possible for given value of l. For example, if l=3, there are 2×3+1 = 7 possible orientations and hence total number of ml values is 7.
‘ml‘ values varies from –l, –l +1, –l +2, …. -2, -1, 0, +1, +2, …. +l -1, +l
For l = 2, possible values of ‘ml‘ are -2, -1, 0, +1, +2. Thus total number of orbitals for given l=2 is 5.
A quick review of relation between subshell and number of orbitals associated with it
| Value of l : | 0 | 1 | 2 | 3 | 4 | 5 | ||
|---|---|---|---|---|---|---|---|---|
| Notation for sub shell : | s | p | d | f | g | h | ||
| Number of orbitals : | 1 | 3 | 5 | 7 | 9 | 11 |