por What is the Moeller diagram?
He moeller diagram it is a graphic and mnemonic method to learn the Madelung rule; that is, how to write the electronic configuration of an element. It is characterized by drawing diagonals through the columns of the orbitals, and following the direction of the arrow, the appropriate order of the same for an atom is established.
In some parts of the world the Moeller diagram is also known as rain method. Through this, an order is defined in the filling of the orbitals, which are defined by the three quantum numbers no, he and ml.
A simple Moeller diagram is shown in the image above. Each column corresponds to different orbitals: s, p, d and f, with their respective energy levels. The arrow indicates that the filling of any atom must begin at the 1s orbital.
Thus, the next arrow should start with the 2s orbital, and then with the 2p passing through the 3s orbital. In this way, as if it were rain, the orbitals and the number of electrons they house are recorded (4he+2).
The Moeller diagram is an introduction for those who study electron configurations.
What is the Moeller diagram?
Madelung’s rule
Since the Moeller diagram is a graphical representation of the Madelung rule, it is necessary to know how the latter works. The filling of the orbitals must obey the following two rules:
– The orbitals with the smallest values of no+he are filled first, being no the principal quantum number, and he the orbital angular momentum. For example, the 3d orbital corresponds to no=3 and he=2, therefore, no+he=3+2=5; while the 4s orbital corresponds to no=4 and he=0, and no+he=4+0=4. From the above it is established that the electrons fill the 4s orbital first than the 3d.
– If two orbitals have the same value of no+hethe electrons will first occupy the one with the lowest value of no. For example, the 3d orbital has a value of no+he=5, the same as the 4p orbital (4+1=5); but since 3d has the least value of noit will be filled first than the 4p.
From the two previous observations, the following order of filling of the orbitals can be reached: 1s 2s 2p 3s 3p 4s 3d 4p.
Following the same steps for different values of no+he for each orbital the electronic configurations of other atoms are obtained; which in turn can also be determined by the Moeller diagram graphically.
Steps to follow
Madelung’s rule states the formula no+he, with which the electronic configuration can be “armed”. However, as stated, the Moeller diagram already graphically represents this; so it is enough to follow its columns and draw diagonals step by step.
It must be taken into account that each type of orbital has a different capacity to house electrons; in this way, we have:
s = 2 electrons
p = 6 electrons
d = 10 electrons
f = 14 electrons
It stops in the orbital where the last electron given by Z has been occupied.
How do you begin the electronic configuration of an atom? To do this, one must first know its atomic number Z, which, by definition, for a neutral atom is equal to the number of electrons.
Thus, with Z we obtain the number of electrons, and with this in mind we begin to draw diagonals through the Moeller diagram.
For further clarification, below are a series of solved exercises.
solved exercises
Beryllium
Using the periodic table, the element beryllium is located with a Z=4; that is, its four electrons must be housed in the orbitals.
Starting then with the first arrow in the Moeller diagram, the 1s orbital occupies two electrons: 1s2; followed by the 2s orbital, with two additional electrons to make 4 total: 2s2.
Therefore, the electronic configuration of beryllium, expressed as [Be] is 1s22s2. Note that the sum of superscripts is equal to the number of total electrons.
Match
The element phosphorus has a Z=15, and consequently, it has 15 electrons in total, which must occupy the orbitals. To go further, start at once with the 1s22s2 configuration, which contains 4 electrons. Then 9 more electrons would be missing.
After the 2s orbital, the next arrow “enters” through the 2p orbital, finally landing in the 3s orbital. Since the 2p orbitals can occupy 6 electrons, and the 3s 2 electrons, we have: 1s22s22p63s2.
There are still 3 more missing electrons, which occupy the following 3p orbital according to the Moeller diagram: 1s22s22p63s23p3, electronic configuration of the phosphor [P].
Zirconium
The zirconium element has a Z=40. Shortening the path with the configuration 1s22s22p63s23p6, with 18 electrons (that of the noble gas argon), then 22 more electrons would be missing.
After the 3p orbital, the next to fill according to the Moeller diagram are the 4s, 3d, 4p, and 5s orbitals.
Filling them completely, that is, 4s2, 3d10, 4p6 and 5s2, adds a total of 20 electrons. The 2 remaining electrons are housed, therefore, in the following orbital: the 4d. Thus, the electron configuration of zirconium [Zr]is: 1s22s22p63s23p64s23d104p65s24d2.
iridium
Iridium has a Z=77, so it has 37 additional electrons compared to zirconium. Starting from [Cd]that is, 1s22s22p63s23p64s23d104p65s24d10, we must add 29 electrons with the following orbitals of the Moeller diagram.
Drawing new diagonals, the new orbitals are: 5p, 6s, 4f and 5d. Filling the first three orbitals completely we have: 5p6, 6s2 and 4f14, to give a total of 22 electrons.
So 7 electrons are missing, which are in the 5d orbital: 1s22s22p63s23p64s23d104p65s24d105p66s24f145d7.
The above is the electronic configuration of iridium, [Ir]. Note that the 6s2 and 5d7 orbitals are highlighted in bold to indicate that they properly correspond to the valence shell of this metal.
Exceptions to the Moeller diagram and the Madelung rule
There are many elements in the periodic table that do not obey what has been explained recently. Their electronic configurations differ experimentally from those predicted for quantum reasons.
Among the elements that present these discrepancies are: chromium (Z=24), copper (Z=29), silver (Z=47), rhodium (Z=45), cerium (Z=58), niobium (Z=41) and many more.
The exceptions are very frequent in the filling of the d and f orbitals. For example, Chromium should have a valence configuration of 4s23d4 according to the Moeller diagram and Madelung’s rule, but it is actually 4s13d5.
Likewise, and finally, the valence configuration of silver should be 5s24d9; but it really is 5s14d10.
References
Mysuperclass (nd) What is electron configuration? Recovered from mysuperclass.com
Moeller diagram. Retrieved from en.wikipedia.org
How to represent electrons in an energy level diagram. Recovered from dummies.com