Download Quantum Mechanics of Atoms: Electron Energy Levels and Electronic Configurations and more Study notes Chemistry in PDF only on Docsity!
Unit 4
Periodicity
Chem 020, R. R. Martin
A. Wave-Particle Duality of Light
Light travels as an electromagnetic wave with a wavelength (λ). The amplitude is the intensity (brightness) The number of cycles that pass a given point per unit time is the frequency (c/λ). One Hertz (Hz) is one cycle per second. The speed ( c ) at which light moves through space is a constant,
2.998 × 10
8 m s
− 1
. Therefore, Frequency = c/λ Electromagnetic waves span a spectrum , but our eyes can only see around 400 – 700 nm. White light from the sun consists of all wavelengths between this range (and more). Work by Max Planck and Albert Einstein in the early 1900’s demonstrated that light can also be considered as a stream of particles known as photons, which have the energy:
E = (hc)/ λ
where h = Planck’s constant, 6.626 × 10
− 34 J s
- Note that the energy of the photon is directly proportional to frequency, yet inversely proportional to wavelength.
o Shorter wavelength = higher frequency = higher energy o Exposure to ultraviolet light and x-rays can cause cancer!
B. Atomic Spectra
Recall that white light consists a continuum of all wavelengths between 400 – 700 nm (the visible region). However, the spectra given off by atoms of gaseous elements consist of lines that are at specific wavelengths, so we obtain a line spectrum (not a continuum). Atomic spectra are characteristic to the element in question, and the spectra can be used for identification purposes. For example, the atomic spectrum of hydrogen can be produced
C. The Bohr Model
In the 1910’s, Neils Bohr developed a Nobel-prize-winning theory to explain the hydrogen spectrum. (While the theory was completely incorrect, it opened doors to the development of the current and accepted quantum mechanical model). Bohr’s assumption was that the electron particle moved in a circular orbit around a central proton and that there were orbits at distinct radial distances (levels) from the proton. Energy would then be released or absorbed as the electron changed orbit levels. Moving the electron further away from the proton requires the addition of energy to overcome the electrostatic forces. Light energy is absorbed (termed excitation ). When an electron moves to a lower level, light energy is released (termed emission ). The energy of the photon emitted corresponds to the difference in energy between the two levels involved.
D. The Quantum Mechanical Model
Although Bohr’s model was highly successful in explaining the line spectrum of the H atom, it failed for everything else. This failure is because Bohr treated the electron like a particle (particles have well- defined paths that can be predicted).
- In 1924, Louis de Broglie suggested that perhaps electrons and light could behave in a similar manner, i.e. perhaps electrons could also behave as both particles and waves o The paths of waves cannot be accurately predicted. This new idea was experimentally confirmed in 1927 at Bell Labs and led to a whole new discipline: quantum mechanics.
- This model differs from the Bohr model in two important ways:
- Because of the particle-wave duality, it is impossible to specify the precise location of an electron at any instant.
- We cannot predict the actual path it takes (not an orbit), and we can only estimate the probability of its position
- The kinetic energy of the electron is inversely related to the volume of the region to which it is confined
- Smaller volume = closer to nucleus. In the smaller volume, electrostatic energy decreases and the kinetic energy decreases The QMM uses complex mathematics to describe the particle- wave behaviour of electrons. However, we won’t look these details…
direction of the electron cloud If ℓ = 0 ( s electron), m ℓ = 0, and there can only be one possible orientation of the s orbital. If ℓ = 1 ( p electron), m ℓ = –1, 0, or +1, and there are three p orbitals each with different orientation
4. Spin Quantum Number ( m s) where m s = +½ or –½ regardless of what the other quantum numbers are When electrons come together, their spins may be the same (both
- or both –) or opposite (one + and one –). These are respectively called parallel spins or opposite spins , and are denoted by arrows pointing up or down.
(parallel, not allowed) ® (opposite, allowed)
- Parallel spins are not allowed because the Pauli Exclusion Principle says that in any one atom, no two electrons may have the same four quantum numbers.
Important note: Each orbital (cloud) can hold two electrons. Thus, if two electrons are in the same orbital, three of their quantum numbers
would be the same. Therefore, to make the 4
th number different, they must have different spins. The max number of electrons for any principle number n is given
by 2 n
2
. ( e.g. if n = 2, we have one s + three p = 8 e
− )
a. Shape of s orbitals
If ℓ = 0 ( s electrons), m ℓ = 0, and there can be only one s orbital at any given principle quantum number n. Recall that a cloud or orbital defines the probability of finding an electron at a particular point (indicated by the dot density). This is
represented by a three-dimensional plot. s orbitals are spherically symmetric. i.e. most of the time, an s electron is found within the sphere drawn on the plot. Realize that every level n has an s orbital and that each one of these orbitals can hold a maximum of two electrons.
o Notation: if, for example, the s orbital on level n = 2 has just one electron, we denote this by the notation 2 s
1
. If it has two electrons (must have opposite spins), then 2 s
2 . b. Shape of p orbitals
If ℓ = 1 ( p electrons), m ℓ = +1, 0, and −1, then there are three p orbitals at every level n ≥ 2. (ℓ = 1 and n = 1 not possible). Each p orbital holds a maximum two electrons, and since there are three of these orbitals, we can have six p electrons at any of the allowed levels ( n ≥ 2). Each p orbital lies on a different axis and features two lobes. Since they are on different axes, they are 90° apart. If, for example, we have six electrons in the p orbitals of level n =
2, we say that it has the configuration 2 p
6
. If only five electrons are
configuration as 1 s
2 2 s
2 2 p
2
o With C, are those two 2 p electrons in the same 2 p orbital or are they in separate ones? (recall three 2 p orbitals) Hund’s Rule states that electrons occupy orbitals of equal energy in such a way that the number of unpaired electrons is at a maximum, thus minimizing inter-electronic repulsion.
- Therefore, in the case of carbon, where we only have two electrons in the 2 p orbitals, those two electrons must reside in different 2 p orbitals. o This is denoted by: 2 _p ____ ____ _____
- Oxygen has 8 electrons, configured 1 s
2 2 s
2 2 p
4 . o Using Hund’s Rule: 2 _p ____ ____ _____ The filling of orbitals using Hund’s Rule gives us the lowest-energy configuration, also called the ground state.
- Other arrangements consistent with the Pauli principle are possible, but are of higher energy. These are called excited states. o Virtually any configuration is possible in an excited state, but the number of electrons does not change.
o An excited state for oxygen could be 1 s
2 2 s
1 2 p
0 3 s
1 3 p
2
Isoelectronic species are those with the same number of electrons arranged similarly. For example, these all have the same configuration has the noble gas Ne (all filled):
o O
2 − , F
− , Ne, Na
, Mg
2+ , Al
3+ are all 1 s
2 2 s
2 2 p
6 or [Ne] a. Orbital energies
In order to write a ground-state configuration, we need to know the energies of the orbitals, or more precisely, the energies of the electrons in the orbitals. There is no absolute fixed energy order, but this is a trend:
- However, in simple cases, we can place electrons into the orbitals in increasing order of n , and for the same n , in increasing order of the orbital quantum number (ℓ). o This approach works for the first 18 electrons. Example:
Argon ground state = 1 s
2 2 s
2 2 p
6 3 s
2 3 p
6
- Subsequent electrons must fill the 4 s level before the 3 d. o Example: K is 1 s
2 2 s
2 2 p
6 3 s
2 3 p
6 4 s
1 shorthand [Ar] 4 s
1
Note: Electrons in the highest n are called valence electrons. The rest are the core electrons. Transition metals, however, behave differently…
- For example, the electronic configuration of Cr (24 electrons) o We would normally predict that the six electrons over the [Ar]
core are arranged 4 s
2 3 d
4
(not the case) o However, if the 3 d orbitals could be exactly half-filled, the 3 d and 4 s become approximately equal in energy. An electron from the 4 s moves to the 3 d , and this scenario also obeys Hund’s Rule and minimizes repulsions. Likewise, completely full 3 d orbitals are favourable, e.g. Cu. The energy of the 3 d falls below that of the 4 s because of the increased
nuclear charge. Cu configuration = [Ar] 4 s
1 3 d
10
Cr and Cu are in the first series of the transition metals. With these, promotion of one electron will always occur if it results in a half- filled or completely filled d orbital. Transition metals in the second series behave similarly.
o Of course, this requires you to know that s holds two electrons, p holds six, d holds ten, and f holds fourteen. However, this same information can be obtained from the periodic table.
F. The Periodic Table and Electronic Configurations
The periodic table is divided into four blocks according to the subshell (ℓ) being filled. It is useful because it allows you to easily determine electronic configuration and which elements may have similar chemical properties. Going across = Groups. Going down = Periods. Main-group elements are those with s or p subshells being filled, with other subshells being full or empty. Those with d orbitals being filled are termed transition elements. Each d sublevel holds 10 electrons. Elements in the f block are those with f orbitals being filled. These
orbitals hold 14 electrons. The lanthanides are those with the 4 f orbitals being filled, and actinides, 5 f. Earlier, we examined the definitions of valence shell (outer) and core electrons (inner). The valence shell is important because these electrons influence the element’s properties. It is also these valence electrons that are used to form bonds. We can determine valence-shell configuration by reading the periodic table from left to right. Using P as an example…
P has the configuration 1 s
2 2 s
2 2 p
6 3 s
2 3 p
3
In shorthand notation, [Ne] 3 s
2 3 p
3
- The number of valence electrons is the number of electrons occupying the highest n level, and in this case five electrons.
- Now repeat with the element As
P has the configuration 1 s
2 2 s
2 2 p
6 3 s
2 3 p
6 4 s
2 3 d
10 4 p
3
In shorthand notation, [Ar] 4 s
2 3 d
10 4 p
3
Number of valence electrons? 5 Notice that As is directly underneath P. Both of these elements are in the same group, #5A (#15). The valence electrons for all elements in the same group have a similar valence configuration. The only difference lies in the identity of n that holds these valence electrons. Since elements in any one group have the same number of valence electrons, it is no surprise that they have similar chemical properties.
Group 1A Alkali metals valence config = ns
1 Li, Na, K, Rb, Cs, Fr
Group 2A Alkali earths valence config = ns
2 Be, Mg, Ca, Sr, Ba,
Ra
Group 3A (13) valence config = ns
2 np
1 B, Al, Ga, In, Tl
Group 4A (14) valence config = ns
2 np
2 C, Si, Ge, Sn, Pb
Group 5A (15) valence config = ns
2 np
3 N, P, As, Sb, Bi
Group 6A (16) Chalcogens valence config = ns
2 np
4 O, S, Se, Te, Po
Group 7A (17) Halogens valence config = ns
2 np
5 F,Cl, Br, I, At
Group 8A (18) Noble Gases valence config = ns
2 np
6 He (1 s
2 ), Ne,
Ar, Kr, Xe, Rn All noble gases have a full valence shell
- Noble gases are extremely stable and not very reactive due to their full valence shell. Other elements can lose or gain electrons to attain the same electronic configuration as these noble gases. o Example: K tends to give away one electron, and Cl can accept an electron to attain the Ar configuration.
- Write electronic configurations for… o I
−
o Sn
2+
o Ru
3+
Which one of these has the greatest number of unpaired electrons
in the ground state? Ge, Cl, Sc
3+ , Br
− , N
12.
G. Periodic Properties of Atoms
1. Atomic Size
- In general, atomic size decreases across a period from left to right, and increases down a group.
12.
These trends can be explained by the concept of effective nuclear charge (Zeff). The outer valence electrons are attracted to the nucleus,
but are also repelled by the core electrons. So, the actual charge that the valence electrons feel is somewhat diminished, and we say that they are shielded by the core electrons. For any electron, Zeff is approximately Z − S, where Z is the actual nuclear charge (atomic number) and S is the number of core electrons. i.e. Zeff = atomic number − # core electrons
11 Na
12 Mg
13 Al Only core electrons shield… valence electrons do not! As Zeff increases across a row, valence electrons are pulled in more tightly, resulting in a smaller atomic size. Going down a group, the number of core electrons increases, which increases the shielding of valence electrons. These valence electrons are less attracted, so size increases.
2. Ionization Energy - The ionization energy (IE) is the energy required to remove an electron completely (infinite separation) from a gas atom
