ToughSTEM
ToughSTEM
A question answer community on a mission
to share Solutions for all STEM major Problems.
Cant find a problem on ToughSTEM?
0
(a) Outline briefly the principles and rules that govern the way in which the ground-state electronic structure of elements varies with increasing atomic number.

(b) Imagine that a scientist reports the synthesis of a new element with atomic number 114. Write down its ground-state electronic structure, using box notation. (Be careful to write the boxes in the correct sequence.) Explain how your answer follows from the rules you have outlined in part (a).

(c) Describe in a few sentences how the Group and Period of an element in the Periodic Table are related to its electronic structure.
Edit
Community
1
Comment
Solutions
0
a) General Rules of Electron Configuration

There are a set of general rules that are used to figure out the electron configuration of an atomic species: Aufbau's Principle, Hund's Rule and the Pauli-Exclusion Principle. Before continuing, it's important to understand that each orbital can be occupied by two electrons of opposite spin (which will be further discussed later). The following table shows the possible number of electrons that can occupy each orbital in a given subshell.

Using our example, iodine, again, we see on the periodic table that its atomic number is 53 (meaning it contains 53 electrons in its neutral state). Its complete electron configuration is 1s22s22p63s23p64s23d104p65s24d105p5. If you count up all of these electrons, you will see that it adds up to 53 electrons. Notice that each subshell can only contain the max amount of electrons as indicated in the table above.

Aufbau Principle

The word 'Aufbau' is German for 'building up'. The Aufbau principle, also called the building-up principle, states that electron's occupy orbitals in order of increasing energy. The order of occupation is as follows:

1s<2s<2p<3s<3p<4s<3d<4p<5s<4d<5p<6s<4f<5d<6p<7s<5f<6d<7p

Another way to view this order of increasing energy is by using Madelung's Rule:
Madelung's Rule is a simple generalization which dictates in what order electrons should be filled in the orbitals, however there are exceptions such as copper and chromium.

This order of occupation roughly represents the increasing energy level of the orbitals. Hence, electrons occupy the orbitals in such a way that the energy is kept at a minimum. That is, the 7s, 5f, 6d, 7p subshells will not be filled with electrons unless the lower energy orbitals, 1s to 6p, are already fully occupied. Also, it is important to note that although the energy of the 3d orbital has been mathematically shown to be lower than that of the 4s orbital, electrons occupy the 4s orbital first before the 3d orbital. This observation can be ascribed to the fact that 3d electrons are more likely to be found closer to the nucleus; hence, they repel each other more strongly. Nonetheless, remembering the order of orbital energies, and hence assigning electrons to orbitals, can become rather easy when related to the periodic table.

To understand this principle, let's consider the bromine atom. Bromine (Z=35), which has 35 electrons, can be found in Period 4, Group VII of the periodic table. Since bromine has 7 valence electrons, the 4s orbital will be completely filled with 2 electrons, and the remaining five electrons will occupy the 4p orbital. Hence the full or expanded electronic configuration for bromine in accord with the Aufbau principle is 1s22s22p63s23p64s23d104p5. If we add the exponents, we get a total of 35 electrons, confirming that our notation is correct.

Hund's Rule

Hund's Rule states that when electrons occupy degenerate orbitals (i.e. same n and l quantum numbers), they must first occupy the empty orbitals before double occupying them. Furthermore, the most stable configuration results when the spins are parallel (i.e. all alpha electrons or all beta electrons). Nitrogen, for example, has 3 electrons occupying the 2p orbital. According to Hund's Rule, they must first occupy each of the three degenerate p orbitals, namely the 2px orbital, 2py orbital, and the 2pz orbital, and with parallel spins (Figure 2). The configuration below is incorrect because the third electron occupies does not occupy the empty 2pz orbital. Instead, it occupies the half-filled 2px orbital. This, therefore, is a violation of Hund's Rule (Figure 2).

Figure Two
A visual representation of the Aufbau Principle and Hund's Rule. Note that the filling of electrons in each orbital (px, py and pz) is arbitrary as long as the electrons are singly filled before having two electrons occupy the same orbital. (a)This diagram represents the correct filling of electrons for the nitrogen atom. (b) This diagram represents the incorrect filling of the electrons for the nitrogen atom.

Pauli-Exclusion Principle

Wolfgang Pauli postulated that each electron can be described with a unique set of four quantum numbers. Therefore, if two electrons occupy the same orbital, such as the 3s orbital, their spins must be paired. Although they have the same principal quantum number (n=3), the same orbital angular momentum quantum number (l=0), and the same magnetic quantum number (ml=0), they have different spin magnetic quantum numbers (ms=+1/2 and ms=-1/2).

Electronic Configurations of Cations and Anions

The way we designate electronic configurations for cations and anions is essentially similar to that for neutral atoms in their ground state. That is, we follow the three important rules: Aufbau's Principle, Pauli-exclusion principle, and Hund's Rule. The electronic configuration of cations is assigned by removing electrons first in the outermost p orbital, followed by the s orbital and finally the d orbitals (if any more electrons need to be removed). For instance, the ground state electronic configuration of calcium (Z=20) is 1s22s22p63s23p64s2. The calcium ion (Ca2+), however, has two electrons less. Hence, the electron configuration for Ca2+ is 1s22s22p63s23p6. Since we need to take away two electrons, we first remove electrons from the outermost shell (n=4). In this case, all the 4p subshells are empty; hence, we start by removing from the s orbital, which is the 4s orbital. The electron configuration for Ca2+ is the same as that for Argon, which has 18 electrons. Hence, we can say that both are isoelectronic.

The electronic configuration of anions is assigned by adding electrons according to Aufbau's building up principle. We add electrons to fill the outermost orbital that is occupied, and then add more electrons to the next higher orbital. The neutral atom chlorine (Z=17), for instance has 17 electrons. Therefore, its ground state electronic configuration can be written as 1s22s22p63s23p5. The chloride ion (Cl-), on the other hand, has an additional electron for a total of 18 electrons. Following Aufbau's principle, the electron occupies the partially filled 3p subshell first, making the 3p orbital completely filled. The electronic configuration for Cl- can, therefore, be designated as 1s22s22p63s23p6. Again, the electron configuration for the chloride ion is the same as that for Ca2+ and Argon. Hence, they are all isoelectronic to each other.
Edit
Community
1
Comment
Close

Choose An Image
or
Get image from URL
GO
Close
Back
Close
What URL would you like to link?
GO
α
β
γ
δ
ϵ
ε
η
ϑ
λ
μ
π
ρ
σ
τ
φ
ψ
ω
Γ
Δ
Θ
Λ
Π
Σ
Φ
Ω
Copied to Clipboard

to interact with the community. (That's part of how we ensure only good content gets on ToughSTEM)
OR
OR
ToughSTEM is completely free, and its staying that way. Students pay way too much already.
Almost done!