Writing Electronic Configuration of an Atom
- Identify the atomic number (\(Z\)) of the atom. The atomic number is equal to the number of protons, which is also equal to the number of electrons in a neutral atom.
- Fill the energy levels (shells) in order of increasing energy. Each energy level is designated by a principal quantum number (\(n\)) starting from 1, 2, 3, and so on.
- Within each energy level, fill the subshells (\(s,p,d,f\)) in order of increasing energy. Each subshell is designated by an azimuthal quantum number (\(l\)) where \(s=0,p=1,d=2,and f=3\).
- Each subshell can hold a certain number of electrons: \(s\) can hold 2, \(p\) can hold 6, \(d\) can hold 10, and \(f\) can hold 14.
Identifying Subshells
Look at the electron configuration. The number before the letter represents the energy level (\(n\)), and the letter represents the subshell (\(l\)).
In quantum mechanics, the type of orbital (\(s,p,d,f\)) is determined by the angular momentum quantum number, which is denoted as \(l\). The values of \(l\) range from 0 to \(n-1\), where \(n\) is the principal quantum number (the shell number). The values of \(l\) correspond to different types of orbitals as follows:
- \(l = 0\) corresponds to an \(s\) orbital.
- \(l = 1\) corresponds to a \(p\) orbital.
- \(l = 2\) corresponds to a \(d\) orbital.
- \(l = 3\) corresponds to an \(f\) orbital.
So, for a given shell number n, you can have:
- \(s\) orbitals for all n (since \(l = 0\) for all n).
- \(p\) orbitals starting from \(n = 2\) (since \(l = 1\) when \(n \geq 2\)).
- \(d\) orbitals starting from \(n = 3\) (since \(l = 2\) when \(n \geq 3\)).
- \(f\) orbitals starting from \(n = 4\) (since \(l = 3\) when \(n \geq 4\)).
Electrons in Each Subshell
Each subshell can hold a certain number of electrons: \(s\) can hold 2, \(p\) can hold 6, \(d\) can hold 10, and \(f\) can hold 14.
The maximum number of electrons that can fit in a subshell is given by the formula \(2(2l+1)\). Here's how it works:
This is derived from quantum mechanics. For example:
- for the \(s\) subshell, where \(l=0\), the formula gives \(2(2\times0+1) = 2\) electrons.
- for the \(p\) subshell, where \(l=1\), the formula gives \(2(2\times1+1) = 6\) electrons.
- for the \(d\) subshell, where \(l=2\), the formula gives \(2(2\times2+1) = 10\) electrons.
- for the \(f\) subshell, where \(l=3\), the formula gives \(2(2\times3+1) = 14\) electrons.
Another approach to understand this:
The number of electrons that each type of orbital can hold is determined by the number of orbital orientations each type has, and the fact that each orbital can hold a maximum of two electrons.
- s orbitals (\(l = 0\)): There is only one s orbital in any given shell, regardless of the shell number. Since each orbital can hold two electrons, an \(s\) orbital can hold a maximum of 2 electrons.
- p orbitals (\(l = 1\)): There are three \(p\) orbitals in any given shell (starting from \(n = 2\)). Each of these orbitals can hold two electrons, so a set of \(p\) orbitals can hold a maximum of 6 electrons (3 orbitals \(\times\) 2 electrons/orbital = 6 electrons).
- d orbitals (\(l = 2\)): There are five \(d\) orbitals in any given shell (starting from \(n = 3\)). Each of these orbitals can hold two electrons, so a set of \(d\) orbitals can hold a maximum of 10 electrons (5 orbitals \(\times\) 2 electrons/orbital = 10 electrons).
- f orbitals (\(l = 3\)): There are seven \(f\) orbitals in any given shell (starting from \(n = 4\)). Each of these orbitals can hold two electrons, so a set of \(f\) orbitals can hold a maximum of 14 electrons (7 orbitals \(\times\) 2 electrons/orbital = 14 electrons).
This pattern continues for higher values of \(l\) (\(g\) orbitals, \(h\) orbitals, etc.), but these orbitals are not occupied in the ground state of the atoms in the periodic table.
Finding Quantum Numbers
- The principal quantum number (\(n\)) is the energy level and can be any positive integer.
- The azimuthal quantum number (\(l\)) is the subshell and can be any integer from 0 to \(n-1\).
- The magnetic quantum number (\(m\)) describes the orientation of the orbital and can be any integer from -l to +l.
- The spin quantum number (\(s\)) describes the spin of the electron and can be \(+1/2\) or \(-1/2\).
Subshell Letters
The letters \(s,p,d,and f\) are used to denote the shape of the orbital. They correspond to \(l=0, 1, 2, and 3\) respectively.
Number of Orbitals
The number of orbitals in a subshell is determined by the azimuthal quantum number (\(l\)). For \(s\) (\(l=0\)), there is 1 orbital; for \(p\) (\(l=1\)), there are 3 orbitals; for \(d\) (\(l=2\)), there are 5 orbitals; and for \(f\) (\(l=3\)), there are 7 orbitals.
The number of orbitals in a subshell is given by \(2l+1\). For example, for the \(p\) subshell where \(l=1\), the formula gives \(2\times1+1 = 3\) orbitals, and so on.
The number of orbitals for each type \((s, p, d, f)\) is determined by the magnetic quantum number \(m_l\), which describes the orientation of the orbital in space. The magnetic quantum number \(m_l\) can have integer values from \(-l\) to \(+l\), including zero.
Here's how it works:
- For \(s\) orbitals (\(l = 0\)), \(m_l\) can only be 0, so there is only one \(s\) orbital.
- For \(p\) orbitals (\(l = 1\)), \(m_l\) can be -1,0,or +1, so there are three \(p\) orbitals.
- For \(d\) orbitals (\(l = 2\)), \(m_l\) can be -2,-1,0,+1,or +2, so there are five \(d\) orbitals.
- For \(f\) orbitals (\(l = 3\)), \(m_l\) can be -3,-2,-1,0,+1,+2,or +3, so there are seven \(f\) orbitals.
This pattern continues for higher values of \(l\) (\(g\) orbitals, \(h\) orbitals, etc.), but these orbitals are not occupied in the ground state of the atoms in the periodic table. Each of these orbitals can hold a maximum of two electrons, which explains why \(s,p,d,and f\) orbitals can hold 2, 6, 10, and 14 electrons respectively.
Electron Spin
The spin quantum number (\(m_s\)) describes the spin of the electron and can be \(+1/2\) or \(-1/2\). This is determined experimentally and does not follow a specific rule. In an orbital, one electron will have a spin of \(+1/2\) and the other will have a spin of \(-1/2\).