Chemistry 068, Chapter 9

Light, Electrons, and Periodic Properties

• In this section we look at the properties of light and electrons.

• We introduce some of the results of quantum mechanics.– Specifically, we look at the Bohr model of the

atom and quantum numbers.

• Lastly we look at several periodic properties.

Wave Nature of Light

• Frequency – the number of wavelengths that pass per unit time. Usually in 1/sec or Hertz (Hz). It is given the symbol ν.

• Wavelength – distance between two identical points on a wave, such as max to max or min to min. It is given the symbol λ.

• The speed of light in a vacuum is c.– c = 2.99792458 x 108 m/sec ≈ 3 x 108 m/sec

• For a light wave, c = νλ. Where ν is in Hz and λ is in meters.

• The energy of a photon is given by:E = hν = hc/λWhere h is Planck’s constant which has a value of

6.626*10-34J*s

Light and Quantum Theory

• Newton viewed light as a beam of particles called photons. This was the predominant view until the twentieth century.

• The current theory of light treats it both as a wave and a particle.– This called the “wave particle duality.”

• This modern theory is coupled to quantum spectroscopy and thus to the quantum theory of the atom.– Electrons also behave with a “wave particle duality,”

but are not photons.

Light Problems

• Calculate the wavelength of a photon with a frequency of 7.5x1015Hz.

• Calculate the frequency of a photon with a wavelength of 635nm.

Light Problems (Cont’d)

• Calculate the energy and frequency of a 365nm photon.

The Electromagnetic spectrum.

Atomic Line Spectra

• The spectra given off by a heated gas is a line spectra – it shows only certain colors (wavelengths) of the EM spectrum.

• Each wavelength corresponds to a different energy transition of the electrons of the atom.

• Hydrogen’s simple spectra was studied extensively by J. J. Balmer.

• For hydrogen, transitions are given by:1/λ = 1.097x107m-1(1/n1

2 – 1/n22)

• And have an energy of:ΔE = -RH(1/nf

2 – 1/ni2)

• Where RH has a value of 2.179x10-18J.

The Bohr Hydrogen Atom

• The Bohr model was developed by physicists Bohr and Rutherford. It was an extension of the work of Planck (energy quanta), Einstein (photo electric effect) and Balmer (atomic spectra).

• It was developed as a way to explain the stability of the atom as well as line spectra.– In the Newtonian view electrons should constantly

loose energy until they collapse into the nucleus.

• The theory was specifically applied to hydrogen, the simplest atom.

• The model has two main postulates.

The Bohr Hydrogen Atom (Cont’d)

• Postulate 1 – Electrons can only have specific energy values called energy levels.

• Likewise, the entire atom can only have specific values.

• This is similar to Planck’s quantized energy levels.

• These energy levels are:

E = -RH/n2 where n = 1, 2, 3, …

The Bohr Hydrogen Atom (Cont’d)

• The ground state corresponds to n = 1.

• Higher n values are farther away from the nucleus.

• Energy lines get closer together as n increases.

• A n value of infinity corresponds to the electron leaving the atom (ionizing).

The Bohr Hydrogen Atom (Cont’d)

• Postulate 2 – Electrons in atoms can change in energy only by going from one level to another.

• These transitions either absorb or emit photons of energy equal to the difference in energy of the two levels.

• This explained Balmer’s atomic spectra.– Distinct because the only photons that could be

emitted corresponded to certain transitions.

Bohr Atom Problems

• What is the wavelength, frequency, and energy of the photon emitted/absorbed during a n=4 to n=1 transition.

• Is a photon emitted or absorbed?

Bohr Atom Problems (Cont’d)

• Calculate the first ionization energy of hydrogen.

Electronic Energy Levels

• Before the early 20th century, the behavior of electrons was poorly understood.

• The development of quantum mechanics lead to a more detailed understanding of electron behavior and electronic structure within the atom.

• The most significant result of our understanding of quantum mechanics was the quantization of the energy levels of the electron.– Quantized quantities can only have certain values,

with no possible values between.

Electron Shells, Subshells, and Orbitals

• The allowed energy levels of the electrons correspond to shells, subshells, and orbitals.

• All of the electrons in a shell have approximately the same energy and are approximately the same distance from the nucleus.– Shell number, n, is a whole number or one or more.

Higher shells are farther away and at higher energy.– The number of electrons in each shell varies. Higher

energy shells hold more electrons.

Electron Shells, Subshells, and Orbitals (Cont’d)

• An electron subshell corresponds to a region in space within a shell where electrons have the same energy.– The number of subshells within a shell is

equal to n.– The shells are lettered s, p, d, f and have the

same number as n.– Subshells increase in energy going from s to

p to d to f.– All subshells of the same letter hold the same

number of electrons.

Electron Shells, Subshells, and Orbitals (Cont’d)

• An orbital is a region of space within a subshell that is likely to hold electrons.– Most of the subshells are actually empty

space.– Each type (letter) of subshell has a different

number of orbitals.– Orbitals of the same type (letter) have similar

shape but different volume.

Electron Spin

• Discovered by Stern and Gerlach in 1921.– Split a beam of atoms (silver, but later other

elements) with a magnetic field.– Half went toward either pole, indicating that

half of the electrons had either charge.

• Since there are two poles, there are two possible values spin.– They correspond to two different directions

that electrons can spin.

The Pauli Exclusion Principle

• No two electrons can have the same combination of four quantum numbers.

• Because there are only two possible spin values, there can only be two electrons in each orbital.

• Thus, each subshell (s, p, d, f) can contain twice as many electrons as it does orbitals.

Summary

n Orbitals #Electrons (2n2)

1 s 2

2 s, p 8

3 s, p, d 18

4 s, p, d, f 32

Etc.

Summary (Cont’d)

Subshell # Orbitals # Electrons

s 1 2

p 3 6

d 5 10

f 7 14

Electron Energy Problems

• In each pair, which shell has a higher energy?

• 5s vs. 2p

• 3s v. 3p

Electron Configuration

• Electron configuration refers to the distribution of electrons within the subshells.

• Written as value n subshell letter # electrons (super scripit). This is repeated for each subshell.

• If an entire n level is filled, it can be abbreviated as [Noble Gas] then the rest of the configuration.– This is called condensed form.– The electrons that make up the noble gas configuration are

called core electrons.– The electrons beyond the noble gas are called outer electrons or

valence electrons.• There are two ways to list d orbitals.

– Some list them before the next s, others after.– For example, 3d10 before 4s1 OR 4s1 then 3d10.– A similar rule exists for f orbitals.

The Aufbau Principle/Hund’s Rule

• Hund’s rule, sometimes called the aufbau principle, states that the lowest energy configuration of electrons in a subshell is attained by placing electrons (of the same spin) in each orbital before pairing electrons up.– The ground state must be the lowest energy

configuration.– Electrons half fill a subshell before they begin to pair

up.• The d and f orbitals are shifted by 1 and 2

respectively when filling.– For example, you fill 4s before 3d and then 4p.– Likewise, you fill 6s then 4f then 5d.

Exceptions to the Rules

• Exceptions occur for the d orbitals (transition metals).

• The (n-1)d orbital will pull one electron out of the ns orbital if the extra electron will completely fill or half fill the d orbital.– Only one electron can be pulled out. So this only

occurs in cases of (n-1)d4ns2 and (n-1)d9ns2; becoming (n-1)d5ns1 and (n-1)d10ns1, respectively.

• This is slightly better energetically, but the two possibilities are very close.

Ions

• Ions are treated as the atom they are isoelectronic to.

• Isoelectronic atoms have the same number of electrons.

Electron Configuration Problems

• Write the electron configuration for the ground state of each of the following atoms.

• He

• U

• O • Fe

Orbital Diagrams

• Orbital diagrams show how the orbitals of a subshell are filled with electrons.

• Circles are drawn for each orbital within a subshell. They are labeled underneath the circle.

• Arrows are used to denote electrons.• Arrows drawn up/down to denote spin (up=+½,

down=-½ ).– Thus there are two electrons in each orbital.

• By convention, up arrows are drawn first.• Again, two ways to list d orbitals.

Orbital Diagram Problems

• Write the orbital diagram for the ground state of each of the following atoms.

• He

• U

• O • Fe

Connection to the Periodic Table

• The Aufbau (building up) principle.– Corresponds to increasing energy levels.– Remember that d is shifted by 1 and f by 2.

• Noble gasses have completely filled shells. Noble gas cores do not normally participate in bonding.

• The electrons outside of the noble gas core are called the valence electrons.– The valence electrons are the electrons which

are involved in chemistry.– The number of valence electrons is very

important in determining chemical properties.

Atomic Orbitals and the Periodic Table

Periodic Properties

• We will look at three periodic properties here.– Atomic radius, the size of an atom.– Ionization energy.– Metallic character.

• Each of these properties follow trends based off of the position of elements on the periodic table.– You can make predictions about which value

is larger/smaller between two atoms based upon their relative positions.

Atomic Radius

• Decreases from left (highest) to right (lowest).– More electrons, but all are pulled in more by the

additional protons.

• Increases from top (lowest) to bottom (largest).– Large increase going from noble gas to valence shell.

• Ions.– Anions (negative ions) are slightly larger than

isoelectronic atom.– Cations (positive ions) are slightly smaller than

isoelectronic atom.

Ionization Energy

• The trend depends on which ionization.– First, second, third, etc. Corresponding to +1, +2, +3, etc. ions.

• For first ionization energy.– Increases left (lowest) to right (highest).

• More protons increases effective nuclear charge that must be overcome.

– Decreases top (highest) to bottom (lowest).• Increased distance from nucleus reduces effective nuclear charge.

• Second (and later) ionization energy follows the same trend except that elements whose second (or later) electron must now be taken out of a noble gas configuration.– Those ionization energies will be the largest, but otherwise

follow the same trend of top/bottom and left/right.• Later ionizations are always larger than first ionizations.

Metallic/Nonmetallic Character

• We can compare how “metallic” different elements are.

• Metallic character decreases from left (highest) to right (lowest).

• Metallic character increases from top (lowest) to bottom (highest).

Periodic Properties Problems

• Arrange the following in order of greatest to least atomic radius.

– Na, Ar, Mg, P, Al, S, Cl, Si

– Li, Cs, K, Na, Fr, Rb

Periodic Properties Problems

• Arrange the following in order of greatest to least first ionization energy and second ionization energy.

– Na, Ar, Mg, P, Al, S, Cl, Si

– Li, Cs, K, Na, Fr, Rb

Periodic Properties Problems

• Arrange the following in order of greatest to least metallic character.

– Na, Ar, Mg, P, Al, S, Cl, Si

– Li, Cs, K, Na, Fr, Rb