The Wave Nature of Light

Waves

• To understand the electronic structure of atoms, one must understand the nature of electromagnetic radiation.

• The distance between corresponding points on adjacent waves is the wavelength ().

Waves

• The number of waves passing a given point per unit of time is the frequency ().

• For waves traveling at the same velocity, the longer the wavelength, the smaller the frequency.

Electromagnetic Radiation

• All electromagnetic radiation travels at the same velocity: the speed of light (c), 3.00 108 m/s.

• Therefore,

c =

The Nature of Energy

• The wave nature of light does not explain how an object can glow when its temperature increases.

• Max Planck explained it by assuming that energy comes in packets called quanta.

The Nature of Energy

• Einstein used this assumption to explain the photoelectric effect.

• He concluded that energy is proportional to frequency:

E = hwhere h is Planck’s constant, 6.63 10−34 J-s.

The Nature of Energy

• Therefore, if one knows the wavelength of light, one can calculate the energy in one photon, or packet, of that light:

c = E = h

The Nature of Energy

Another mystery involved the emission spectra observed from energy emitted by atoms and molecules.

The Nature of Energy

• One does not observe a continuous spectrum, as one gets from a white light source.

• Only a line spectrum of discrete wavelengths is observed.

The Nature of Energy

• Niels Bohr adopted Planck’s assumption and explained these phenomena in this way:1. Electrons in an atom can only

occupy certain orbits (corresponding to certain energies).

The Nature of Energy

• Niels Bohr adopted Planck’s assumption and explained these phenomena in this way:2. Electrons in permitted orbits

have specific, “allowed” energies; these energies will not be radiated from the atom.

The Nature of Energy

• Niels Bohr adopted Planck’s assumption and explained these phenomena in this way:3. Energy is only absorbed or

emitted in such a way as to move an electron from one “allowed” energy state to another; the energy is defined by

E = h

The Nature of Energy

The energy absorbed or emitted from the process of electron promotion or demotion can be calculated by the equation:

E = −RH ( )1nf2

1ni2

-

where RH is the Rydberg constant, 2.18 10−18 J, and ni and nf are the initial and final energy levels of the electron.

The Wave Nature of Matter

• Louis de Broglie posited that if light can have material properties, matter should exhibit wave properties.

• He demonstrated that the relationship between mass and wavelength was

=hmv

Atomic Electron Configurations

Electron spin

1. Quantum number (ms) – electron spin magnetic quantum number

2. To totally understand this, we must first learn about magnetism.

Paramagnetism and Unpaired Electrons

Substances are:

Diamagnetic if they are repelled by a strong magnet

Paramagnetic if they are attracted by a magnet

Electron spins1. Paramagnetism arises from electron

spins.

2. Electron spins have 2 orientations

3. Therefore, the electron spin is quantized and can have a quantum number

4. Possible values: ms = + ½ or – ½

Paramagnetism and diamagnetism

• Paramagnetism occurs in substances in which the ions or atoms have unpaired electrons

• Diamagnetism occurs in substances in which the ions or atoms have paired electrons

Pauli Exclusion Principle

• No two electrons in an atom can have the same set of four quantum numbers.

• No atomic orbital can contain more than two electrons.

What are the possible numbers of electrons in….

The s orbitals: 2

The p orbitals: 6

The d orbitals: 10

The f orbitals: 14

Aufbau Principle

• Electrons are placed in the lowest energetically available subshell.

• An orbital can hold at most 2 electrons.• If two or more energetically equivalent

orbitals are available (e.g., p, d etc.) then electrons should be spread out before they are paired up (Hund's rule).

Atomic energy diagram

Which of the subshells should be filled first?

Order of orbital filling

Types of Notations and Valence Electrons

• 3 types:

Electron Configuration

Na:

Noble gas notations

Na:

Orbital notations

Exceptions to the Rule

• Cr

• Cu

Electron configurations of ions (excited state)

• Rules:

• Remove electrons from the electron shell of the highest n

• If there is a choice of a subshell within the nth subshell, the electron electrons are removed from the maximum l.

E- Configurations of Ions

• Tin

• Tin2+

• Tin4+

Quantum Mechanical Model of the Atom

Erwin Schrödinger

• Professor of physics!

• Wrote daring equations!

• Confounded his critics!

The quantum mechanical atom

• It is impossible to specify the precise position of an electron in an atom at a given instant – Heisenberg Uncertainty Principle

Quantum Numbers

• Every electron in an atom has a set of four quantum numbers.

• Pauli Exclusion Principle – No two electrons in an atom can have the same set of four quantum numbers.

First Quantum Number (n)

• Principle energy level

• n = 1, 2, 3, 4, etc.

• As n increases, the electron is farther out from the nucleus.

Second quantum number (l)

• Each principal energy level includes one or more sublevels.

• l = the shape of the orbital (s, p, d, f)

• l : 0 to n-1

Quantum number l

Type of sublevel

0 s

1 p

2 d

3 f

Third quantum number ml

• Each sublevel contains one or more orbitals.

• ml determines the direction in space of the electron cloud surrounding the nucleus (orientation of the orbital).

• -l to l

ml = -1 ml = 0 ml = 1

ml = -2 ml = -1 ml = 0 ml = 1 ml = 27.6

Fourth quantum number ms

• Associated with electron spin.

• An electron has magnetic properties that correspond to those of a charged particle spinning on its axis.

• ms = +1/2 or -1/2

Ex

• For principal quantum level n=5, determine the number of allowed subshells, and give the designation of each.

Ex

• Which of the following sets of quantum numbers are not allowed in the hydrogen atom?

a. n=2, l =1, ml = -1

b. n=1, l =1, ml = 0

c. n=8, l =7, ml = -6

d. n=1, l =0, ml = 2

Ex

• Give a possible set of values of the four quantum numbers for all the electrons in a Boron atom

Ex

• Give a possible set of values of the four quantum numbers for all the electrons in a nitrogen atom if each is in the ground state

Ex

• Which of the following electron configurations correspond to an excited state? Identify the atoms and write the ground state electron configuration where appropriate.

a. 1s22s23p1

b. 1s22s22p6

c. 1s22s22p43s1

d. [Ar]4s23d54p1

E- Configuration Battleship

• s-sublevel – Destroyer – • p-sublevel – Cruiser – • d-sublevel – Battleship –