Quantum Numbers and their significance
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.
Total number of orbitals present in nth shell is n2. Total number of electrons that can be present in nth shell is 2 × n2.
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 also factors in while calculating energy of an orbital in a multi electron system. 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
Total number of orbitals present in lth sub-shell is 2l +1. Total number of electrons that can be present in lth sub-shell is 2 × (2l +1). It also accounts for the fine lines present in the atomic spectra.
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
It also accounts for the splitting of lines in the atomic spectra on application of electric and magnetic fields.
Possibility of only two spins shows that an orbital cannot have more than two electrons each having opposite spins. It explains the presence of doublets (two lines closely spaced) and triplets(three lines closely spaced) etc. of multi electron atoms.
<img src="https://latex.codecogs.com/svg.image?E_n = -13.6 frac{Z^2}{n^2} eV = -2.18times10^{-18} frac{Z^2}{n^2} J"
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.
Total number of orbitals present in nth shell is n2. Total number of electrons that can be present in nth shell is 2 × n2.
| 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 also factors in while calculating energy of an orbital in a multi electron system. 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 | … |
Subshell Notations
Total number of orbitals present in lth sub-shell is 2l +1. Total number of electrons that can be present in lth sub-shell is 2 × (2l +1). It also accounts for the fine lines present in the atomic spectra.
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
It also accounts for the splitting of lines in the atomic spectra on application of electric and magnetic fields.
| 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 |
Electron Spin Quantum Number (ms)
It refers to spin angular momentum of an electron due to its spinning around its axis. The momentum being a vector quantitiy has two orientation relative to chosen axis. These two oientations are distinguished by the spin quantum numbers ms, value being +1/2 and -1/2. These two spins states are normally represented by two arrows ↑ (spin up) and ↓ (spin down).Possibility of only two spins shows that an orbital cannot have more than two electrons each having opposite spins. It explains the presence of doublets (two lines closely spaced) and triplets(three lines closely spaced) etc. of multi electron atoms.
Summary – Quantum Numbers
Principal Quantum NumberProposed by Neil Bohr
Infromation about main energy level called Shell
Size of the orbital
<img src="https://latex.codecogs.com/svg.image?E_n = 52.9 frac{n^2}{Z} pm"
<img src="https://latex.codecogs.com/svg.image?E_n = -13.6 frac{Z^2}{n^2} eV = -2.18times10^{-18} frac{Z^2}{n^2} J"
| Shell = | K | L | M | N | … | |
|---|---|---|---|---|---|---|
| n = | 1 | 2 | 3 | 4 | … |
