Quantum NumbersGeneral rule of Electron configuration

The electron configuration of an atomic varieties (neutral or ionic) permits us to recognize the shape and also energy of its electrons. Numerous general rules space taken into consideration when assigning the "location" that the electron come its prospective energy state, yet these assignments are arbitrary and it is constantly uncertain as to which electron is being described. Discovering the electron configuration of a species gives united state a much better understanding that its bonding ability, magnetism and also other rememberingsomer.comical properties.

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Introduction

The electron configuration is the typical notation provided to describe the digital structure of an atom. Under the orbital approximation, we let each electron accounting an orbital, which deserve to be fixed by a single wavefunction. In act so, we obtain three quantum numbers (n,l,ml), which are the exact same as the ones acquired from solving the Schrodinger"s equation for Bohr"s hydrogen atom. Hence, plenty of of the rules the we use to explain the electron"s address in the hydrogen atom can likewise be supplied in systems including multiple electrons. As soon as assigning electron to orbitals, we need to follow a set of 3 rules: the Aufbau Principle, the Pauli-Exclusion Principle, and Hund"s Rule.

The wavefunction is the solution to the Schrödinger equation. By addressing the Schrödinger equation for the hydrogen atom, we acquire three quantum numbers, namely the principal quantum number (n), the orbit angular inert quantum number (l), and the magnetic quantum number (ml). There is a 4th quantum number, called the rotate magnetic quantum number (ms), i beg your pardon is not acquired from solving the Schrödinger equation. Together, these 4 quantum numbers have the right to be provided to describe the place of one electron in Bohr"s hydrogen atom. This numbers have the right to be thought of together an electron"s "address" in the atom.


Notation

To help describe the proper notation because that electron configuration, that is ideal to execute so with example. Because that this example, us will usage the iodine atom. There space two means in i beg your pardon electron configuration deserve to be written:

I: 1s22s22p63s23p64s23d104p65s24d105p5

or

I: 5s24d105p5

In both that these species of notations, the stimulate of the power levels have to be composed by increased energy, reflecting the variety of electrons in each subshell together an exponent. In the quick notation, you place brackets roughly the preceding noble gas facet followed through the valence covering electron configuration. The regular table mirrors that kyrpton (Kr) is the ahead noble gas detailed before iodine. The noble gas configuration encompases the power states lower than the valence covering electrons. Therefore, in this instance =1s22s22p63s23p64s23d104p6.


Principal Quantum Number (n)

The principal quantum number n suggests the shell or energy level in i m sorry the electron is found. The value of n have the right to be collection between 1 come n, wherein n is the worth of the outermost covering containing one electron. This quantum number have the right to only it is in positive, non-zero, and integer values. That is, n=1,2,3,4,..

For example, an Iodine atom has its outmost electrons in the 5p orbital. Therefore, the principle quantum number for Iodine is 5.


Orbital Angular momentum Quantum Number (l)

The orbit angular momentum quantum number, l, suggests the subshell the the electron. Friend can also tell the form of the atomic orbital with this quantum number. An s subshell synchronizes to l=0, a p subshell = 1, a d subshell = 2, a f subshell = 3, and also so forth. This quantum number can only it is in positive and integer values, return it have the right to take on a zero value. In general, for every worth of n, there room n worths of l. Furthermore, the value of l varieties from 0 to n-1. For example, if n=3, l=0,1,2.

So in regards come the example used above, the l values that Iodine for n = 5 are l = 0, 1, 2, 3, 4.


Magnetic Quantum Number (ml)

The magnetic quantum number, ml, to represent the orbitals that a given subshell. Because that a provided l, ml can variety from -l to +l. A ns subshell (l=1), for instance, deserve to have three orbitals corresponding to ml = -1, 0, +1. In various other words, it specifies the px, py and also pzorbitals the the ns subshell. (However, the ml numbers don"t necessarily exchange mail to a offered orbital. The reality that there are three orbitals simply is indicative that the three orbitals the a p subshell.) In general, for a offered l, there space 2l+1 feasible values for ml; and also in a n principal shell, there room n2 orbitals found in that power level.

Continuing on from out instance from above, the ml values of Iodine space ml = -4, -3, -2, -1, 0 1, 2, 3, 4. These arbitrarily exchange mail to the 5s, 5px, 5py, 5pz, 4dx2-y2, 4dz2, 4dxy, 4dxz, and also 4dyz orbitals.


Spin Magnetic Quantum Number (ms)

The spin magnetic quantum number have the right to only have a value of one of two people +1/2 or -1/2. The value of 1/2 is the turn quantum number, s, which describes the electron"s spin. Due to the rotate of the electron, it generates a magnetic field. In general, an electron through a ms=+1/2 is called ­­an alpha electron, and also one v a ­ms=-1/2 is referred to as a beta electron. No 2 paired electrons have the right to have the exact same spin value.

Out the these four quantum numbers, however, Bohr postulated that just the primary quantum number, n, identify the energy of the electron. Therefore, the 3s orbital (l=0) has the same energy as the 3p (l=1) and 3d (l=2) orbitals, nevertheless of a distinction in l values. This postulate, however, stop true just for Bohr"s hydrogen atom or other hydrogen-like atoms.

When managing multi-electron systems, us must think about the electron-electron interactions. Hence, the previously described postulate breaks down in the the energy of the electron is now identified by both the major quantum number, n, and also the orbital angular inert quantum number, l. Return the Schrodinger equation because that many-electron atom is extremely challenging to solve mathematically, we have the right to still explain their digital structures via electron configurations.


General rule of Electron Configuration

There space a set of general rules that are supplied to number out the electron configuration of an atom species: Aufbau Principle, Hund"s Rule and the Pauli-Exclusion Principle. Prior to continuing, it"s vital to know that each orbital can be lived in by two electrons of opposite turn (which will certainly be further discussed later). The complying with table shows the possible number of electrons that have the right to occupy every orbital in a given subshell.

subshell number the orbitals total variety of possible electron in every orbital
s 1 2
p 3 (px, py, pz) 6
d 5 (dx2-y2, dz2, dxy, dxz, dyz) 10
f 7 (fz3, fxz2, fxyz, fx(x2-3y2), fyz2, fz(x2-y2), fy(3x2-y2)

14

Using our example, iodine, again, we watch on the regular table that its atom number is 53 (meaning it includes 53 electron in its neutral state). Its complete electron configuration is 1s22s22p63s23p64s23d104p65s24d105p5. If you counting up all of these electrons, you will view that that adds approximately 53 electrons. Notice that each subshell can only contain the max quantity of electron as suggested in the table above.


Aufbau Principle

The indigenous "Aufbau" is German because that "building up". The Aufbau Principle, also called the building-up principle, says that electron"s occupy orbitals in stimulate of boosting energy. The order of occupation is together follows:

1s

*

Hund"s preeminence states that once electrons occupy degenerate orbitals (i.e. Same n and also l quantum numbers), castle must very first occupy the north orbitals before double occupying them. Furthermore, the many stable construction results when the spins are parallel (i.e. All alpha electron or all beta electrons). Nitrogen, for example, has actually 3 electron occupying the 2p orbital. According to Hund"s Rule, castle must very first occupy each of the 3 degenerate ns orbitals, namely the 2px orbital, 2py orbital, and also the 2pz orbital, and also with parallel spins (Figure 2). The configuration below is incorrect since the 3rd electron rectal does no occupy the north 2pz orbital. Instead, it occupies the half-filled 2px orbital. This, therefore, is a violation of Hund"s preeminence (Figure 2).

*
Figure 2. A visual representation of the Aufbau Principle and also Hund"s Rule. Keep in mind that the pour it until it is full of electrons in each orbital(px, py and also pz) is arbitrary as lengthy as the electrons space singly filled before having two electrons accounting the very same orbital.(a)This diagram to represent the correct filling of electrons for the nitrogen atom. (b) This diagramrepresents the incorrectfilling of the electrons for the nitrogen atom.



Electronic construction of Cations and also Anions

The way we designate digital configurations because that cations and also anions is essentially similar to the for neutral atoms in their ground state. That is, we follow the three vital rules: Aufbau Principle, Pauli-exclusion Principle, and also Hund"s Rule. The digital configuration the cations is assigned by removing electrons very first in the outermost p orbital, adhered to by the s orbital and also finally the d orbitals (if any an ext electrons have to be removed). Because that instance, the floor state digital configuration the calcium (Z=20) is 1s22s22p63s23p64s2. The calcium ion (Ca2+), however, has actually two electrons less. Hence, the electron construction for Ca2+ is 1s22s22p63s23p6. Since we must take away two electrons, we very first remove electrons from the outermost shell (n=4). In this case, all the 4p subshells room empty; hence, we start by removing from the s orbital, i m sorry is the 4s orbital. The electron construction for Ca2+ is the very same as that for Argon, which has 18 electrons. Hence, we have the right to say that both room isoelectronic.

The digital configuration the anions is assigned by including electrons follow to Aufbau Principle. We include electrons to fill the outermost orbital the is occupied, and also then add much more electrons come the next greater orbital. The neutral atom chlorine (Z=17), for instance has actually 17 electrons. Therefore, its soil state electronic configuration deserve to be written as 1s22s22p63s23p5. The chloride ion (Cl-), top top the other hand, has an additional electron because that a total of 18 electrons. Following Aufbau Principle, the electron rectal the partially filled 3p subshell first, making the 3p orbital completely filled. The digital configuration because that Cl- can, therefore, be designated together 1s22s22p63s23p6. Again, the electron configuration for the chloride ion is the exact same as that for Ca2+ and Argon. Hence, they room all isoelectronic to each other.


Problems

1. I m sorry of the princples explained over tells united state that electron that are paired cannot have the same spin value?

2. Discover the worths of n, l, ml, and also ms for the following:

a. Mg

b. Ga

c. Co

3. What is a possible combination for the quantum numbers of the 5d orbital? Give an instance of an aspect which has actually the 5d orbital as it"s many outer orbital.

4. I beg your pardon of the complying with cannot exist (there may be much more than one answer):

a. N = 4; l = 4; ml = -2; ms = +1/2

b. N = 3; l = 2; ml = 1; ms = 1

c. N = 4; l = 3; ml = 0; multiple sclerosis = +1/2

d. N = 1; l = 0; ml = 0; ms = +1/2

e. N = 0; l = 0; ml = 0; ms = +1/2

5. Write electron configurations for the following:

a. P

b. S2-

c. Zn3+


Answers

1. Pauli-exclusion Principle

2. A. N = 3; l = 0, 1, 2; ml = -2, -1, 0, 1, 2; ms deserve to be one of two people +1/2 or -1/2

b. N = 4; l = 0, 1, 2, 3; ml = -3, -2, -1, 0, 1, 2, 3; ms deserve to be one of two people +1/2 or -1/2

c. N = 3; l = 0, 1, 2; ml = -2, -1, 0, 1, 2, 3; ms have the right to be either +1/2 or -1/2

3. N = 5; l = 3; ml = 0; ms = +1/2. Osmium (Os) is an example.

4. A. The value of l can not be 4, because l arrays from (0 - n-1)

b. Ms have the right to only it is in +1/2 or -1/2

c. Okay

d. Okay

e. The value of n cannot be zero.

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5. A. 1s22s22p63s23p3

b. 1s22s22p63s23p6

c. 1s22s22p63s23p64s23d7


References

Atkins, P. W., & De Paula, J. (2006). Physical rememberingsomer.comistry for the Life Sciences. new York, NY: W. H. Freeman and Company. Petrucci, R. H., Harwood, W. S., & Herring, F. G. (2002). General rememberingsomer.comistry: ethics and modern-day Applications. upper Saddle River, NJ: Prentice-Hall, Inc. Shagoury, Richard. rememberingsomer.comistry 1A class Book. 4th Ed. Custom Publishing. 2006. Print