Electronic Structure of Atoms Chapter 6. Introduction Almost all chemistry is driven by electronic...

Electronic Structure of Atoms

Chapter 6

Introduction

• Almost all chemistry is driven by electronic structure, the arrangement of electrons in atoms

• What are electrons like?

• Our understanding of electrons has developed greatly from quantum mechanics

6.1 Wave Nature of Light

• If we excite an atom, light can be emitted.

• This nature of this light is defined by the electron structure of the atom in question

– light given off by H is different from that by He or Li, etc.

– Each element is unique

6.1 Wave Nature of Light

• The light that we can see (visible light) is only a small portion of the “electromagnetic spectrum”

• Visible light is a type of “electromagnetic radiation” (it contains both electric and magnetic components)

• Other types include radio waves, x-rays, UV rays, etc. (fig. 6.4)

The Wave Nature of LightThe Wave Nature of Light

The Wave Nature of Light• All waves have a characteristic

wavelength, , and amplitude, A.

• The frequency, , of a wave is the number of cycles which pass a point in one second.

• The speed of a wave, v, is given by its frequency multiplied by its wavelength: For light, speed = c.

c =

c vs. vs. • The longer the wavelength, the fewer cycles are

seen

• c = x

• radio station KDKB-FM broadcasts at a frequency of 93.3 MHz. What is the wavelength of the radio waves?

Quantized Energy and Photons

• Classical physics says that changes occur continuously

• While this works on a large, classical theories fail at extremely small scales, where it is found that changes occur in discrete quantities, called quanta

• This is where quantum mechanics comes into play

Quanta

• We know that matter is quantized.

– At a large scale, pouring water into a glass appears to proceed continuously. However, we know that we can only add water in increments of one molecule

• Energy is also quantized

– There exists a smallest amount of energy that can be transferred as electromagnetic energy

Quantization of light

• A physicist named Max Planck proposed that electromagnetic energy is quantized, and that the smallest amount of electromagnetic energy that can be transferred is related to its frequency

Quantization of light• E = h

– h = 6.63 x 10-34 J.s (Planck's constant)– Electromagnetic energy can be transferred in

inter multiples of h. (2h, 3h, ...)

• To understand quantization consider the notes produced by a violin (continuous) and a piano (quantized):– a violin can produce any note by placing the

fingers at an appropriate spot on the bridge. – A piano can only produce notes corresponding

to the keys on the keyboard.

Photoelectric effect

• If EM radiation is shined upon a clean metal surface, electrons can be emitted

• For any metal, there is a minimum frequency below which no electrons are emitted

• Above this minimum, electrons are emitted with some kinetic energy

• Einstein explained this by proposing the existence of photons (packets of light energy)– The Energy of one photon, E = hν.

Quantized Energy and PhotonsQuantized Energy and Photons

The Photoelectric EffectThe Photoelectric Effect

Sample

• Calculate the energy of one photon of yellow light whose wavelength is 589 nm

Sample Problems

• A violet photon has a frequency of 7.100 x 1014 Hz. – What is the wavelength (in nm) of the photon?

– What is the wavelength in Å?

– What is the energy of the photon?

– What is the energy of 1 mole of these violet photons?

Free Response Type Question

• Chlorophyll a, a photosynthetic pigment found in plants, absorbs light with a wavelength of 660 nm.

– Determine the frequency in Hz– Calculate the energy of a photon of light with

this wavelength

Bohr’s Model of the Hydrogen Atom Bohr’s Model of the Hydrogen Atom Radiation composed of only one wavelength is called monochromatic.

•Radiation that spans a whole array of different wavelengths is called continuous.

•White light can be separated into a continuous spectrum of colors.

•If we pass white light through a prism, we can see the “continuous spectrum” of visible light (ROYGBIV)•Some materials, when energized, produce only a few distinct frequencies of light

•neon lamps produce a reddish-orange light•sodium lamps produce a yellow-orange light

These spectra are called “line spectra

Bohr’s Model of the Hydrogen AtomBohr’s Model of the Hydrogen Atom

Line SpectraLine Spectra

Shows that visible light contains many wavelengths

Bohr’s Model of the Hydrogen Atom Bohr’s Model of the Hydrogen Atom

Bohr’s ModelBohr’s ModelColors from excited gases arise because electrons move between energy states in the atom.

Only a few wavelengths emitted from elements


Bohr’s ModelBohr’s ModelSince the energy states are quantized, the light emitted from excited atoms must be quantized and appear as line spectra.After lots of math, Bohr showed that

E = (-2.18 x 10-18 J)(1/n2)Where n is the principal quantum number (i.e., n = 1, 2, 3, …. and nothing else)

“ground state” = most stable (n = 1)“excited state” = less stable (n > 1)When n = ∞, En = 0

Bohr Model• To explain line spectrum of hydrogen, Bohr proposed that

electrons could jump from energy level to energy level

– When energy is applied, electron jumps to a higher energy level– When electron jumps back down, energy is given off in the form of light– Since each energy level is at a precise energy, only certain amounts of

energy (E = Ef – E

i) could be emitted

– I.e. hEEE if

E photon h RH 1

nlower2

1

nupper2


Bohr’s ModelBohr’s ModelWe can show that

E = (-2.18 x 10-18 J)(1/nf2 - 1/ni

2 )

When ni > nf, energy is emitted.When nf > ni, energy is absorbed.

Sample calculation (Free Response Type Question)

• In the Balmer series of hydrogen, one spectral line is associate with the transition of an electron from the fourth energy level (n=4) to the second energy level n=2.

– Indicate whether energy is absorbed or emitted as the electron moves from n=4 to n=2. Explain (there are no calculations involved)

– Determine the wavelength of the spectral line.

– Indicate whether the wavelength calculated in the previous part is longer or shorter than the wavelength assoicated with an electron moving from n=5 to n=2. Explain (there are no calculations involved)

Wave Behavior of Matter• EM radiation can behave like waves or particles

• Why can't matter do the same?

• Louis de Broglie made this very proposal

– Using Einstein’s and Planck’s equations, de Broglie supposed:

vm

h

What does this mean?

• In one equation de Broglie summarized the concepts of waves and particles as they apply to low mass, high speed objects

• As a consequence we now have:– X-Ray diffraction– Electron microscopy

Sample Exercise

• Calculate the wavelength of an electron traveling at a speed of 1.24 x 107 m/s. The mass of an electron is 9.11 x 10-28 g.

Heisenberg’s Uncertainty PrincipleHeisenberg’s Uncertainty Principle: on the mass scale of atomic particles, we cannot determine the exactly the position, direction of motion, and speed simultaneously.For electrons: we cannot determine their momentum and position simultaneously.

The Uncertainty Principle

Quantum Mechanics and Atomic Quantum Mechanics and Atomic OrbitalsOrbitals

•Schrödinger proposed an equation that contains both wave and particle terms.

•Solving the equation leads to wave functions.

•The wave function gives the shape of the electronic orbital.

•The square of the wave function, gives the probability of finding the electron, that is, gives the electron density for the atom.


If we solve the Schrödinger equation, we get wave

functions and energies for the wave functions.We call wave functions orbitalsorbitals.

Schrödinger’s equation requires 3 quantum numbers:Principal Quantum Number, n. This is the same as Bohr’s n.

As n becomes larger, the atom becomes larger and the

electron is further from the nucleus.

Orbitals and Quantum NumbersOrbitals and Quantum NumbersAzimuthal Quantum Number, l. Shape This quantum

number depends on the value of n. The values of l

begin at 0 and increase to (n - 1). We usually use

letters for l (s, p, d and f for l = 0, 1, 2, and 3).

Usually we refer to the s, p, d and f-orbitals.

Magnetic Quantum Number, ml direction This

quantum number depends on l. The magnetic

quantum number has integral values between -l and

+l (including 0). Magnetic quantum numbers give

the 3D orientation of each orbital.

Orbitals and Quantum NumbersOrbitals and Quantum Numbers

Restrictions

• The shell with principal quantum number n will consist of exactly n subshells. Each shell corresponds to a different allowed value of l from 0 to n-1

– Therefore the first shell consists of only 1 subshell, the second shell consists of only 2 subshells….

Restrictions

• Each subshell consists of a specific number of orbitals. Each orbital corresponds to a different allowed value of ml. For a given value of l, there are 2l+1 allowed values of ml , ranging from –l to +l

• Therefore each s subshell consists of one orbital, each p consists of three orbitals….

Restrictions

• The total number of orbitals in a shell is n2

where n is the principal quantum number of the shell

Sample Exercise

• Which element (s) has an outermost electron that could be described by the following quantum numbers (3, 1, -1, ½ )?

You Try

• Which element (s) has an outermost electron that could be described by the following quantum numbers (4, 0, 0, ½)


Orbitals can be ranked in terms of energy to yield an Aufbau diagram.

Note that the following Aufbau diagram is for a single electron system.

As n increases, note that the spacing between energy levels becomes smaller.

Representation of OrbitalsRepresentation of OrbitalsThe The ss Orbitals Orbitals

All s-orbitals are spherical.

As n increases, the s-orbitals get larger.

As n increases, the number of nodes increase.

A node is a region in space where the probability of finding an electron is zero.

At a node, 2 = 0

For an s-orbital, the number of nodes is (n - 1).

Representation of OrbitalsRepresentation of Orbitals

The The ss Orbitals Orbitals


The The pp Orbitals Orbitals

There are three p-orbitals px, py, and pz. (The three p-orbitals lie

along the x-, y- and z- axes. The letters correspond to allowed

values of ml of -1, 0, and +1.)

The orbitals are dumbbell shaped.

As n increases, the p-orbitals get larger.

All p-orbitals have a node at the nucleus.


The The pp Orbitals Orbitals


The The dd and and ff Orbitals Orbitals

There are 5 d- and 7 f-orbitals.

Three of the d-orbitals lie in a plane bisecting the x-, y- and z-axes.

Two of the d-orbitals lie in a plane aligned along the x-, y- and z-axes.

Four of the d-orbitals have four lobes each.

One d-orbital has two lobes and a collar.

Representation of OrbitalsRepresentation of OrbitalsThe The dd Orbitals Orbitals

Orbitals in Many Electron AtomsOrbitals in Many Electron Atoms

Orbitals of the same energy are said to be degenerate.

All orbitals of a given subshell have the same energy (are degenerate)

For example the three 4p orbitals are degenerate


Energies of OrbitalsEnergies of Orbitals

Orbitals in Many Electron AtomsOrbitals in Many Electron AtomsElectron Spin and the Pauli Exclusion PrincipleElectron Spin and the Pauli Exclusion Principle

•Line spectra of many electron atoms show each line as a closely spaced pair of lines.

•Stern and Gerlach designed an experiment to determine why.•A beam of atoms was passed through a slit and into a magnetic field and the atoms were then detected.

•Two spots were found: one with the electrons spinning in one direction and one with the electrons spinning in the opposite direction.


Electron Spin and the Pauli Exclusion PrincipleElectron Spin and the Pauli Exclusion Principle


Electron Spin and the Pauli Exclusion PrincipleElectron Spin and the Pauli Exclusion Principle

Since electron spin is quantized, we define ms = spin

quantum number = ½.

Pauli’s Exclusions Principle:Pauli’s Exclusions Principle: no two electrons can have

the same set of 4 quantum numbers.

Therefore, two electrons in the same orbital must have

opposite spins.

Electron configurations tells us in which orbitals the electrons for an element are located.

Three rules:•electrons fill orbitals starting with lowest n and moving upwards

•no two electrons can fill one orbital with the same spin (Pauli)

•for degenerate orbitals, electrons fill each orbital singly before any orbital gets a second electron (Hund’s rule).

Electron Configurations

Details

• Valence electrons- the electrons in the outermost energy levels (not d).

• Core electrons- the inner electrons.

• C 1s2 2s2 2p2

Fill from the bottom up following the arrows

1s2s 2p3s 3p 3d4s 4p 4d 4f

5s 5p 5d 5f6s 6p 6d 6f7s 7p 7d 7f

• 1s2

• 2• electrons

2s2

• 4

2p6 3s2

• 12

3p6 4s2

• 20

3d10 4p6

5s2

• 38

4d10 5p6 6s2

• 56

Electron Configurations and the Periodic Electron Configurations and the Periodic TableTable

Electron Configurations and the Periodic Electron Configurations and the Periodic TableTable

There is a shorthand way of writing electron configurations

Write the core electrons corresponding to the filled Noble gas in square brackets.

Write the valence electrons explicitly.

Example, P: 1s22s22p63s23p3

but Ne is 1s22s22p6

Therefore, P: [Ne]3s23p3.

Exceptions

• Ti = [Ar] 4s2 3d2

• V = [Ar] 4s2 3d3

• Cr = [Ar] 4s1 3d5

• Mn = [Ar] 4s2 3d5

• Half filled orbitals.

• Scientists aren’t sure of why it happens

• same for Cu [Ar] 4s1 3d10

More exceptions

• Lanthanum La: [Xe] 6s2 5d1

• Cerium Ce: [Xe] 6s2 4f1 5d1

• Promethium Pr: [Xe] 6s2 4f3 5d0

• Gadolinium Gd: [Xe] 6s2 4f7 5d1

• Lutetium Pr: [Xe] 6s2 4f14 5d1

Diamagnetism and Paramagnetism

• Diamagnetism– Repelled by magnets– Occurs in elements

where all electrons are paired

– Usually group IIA or noble gases

• Paramagnetism– Attracted to magnets– Occurs in elements

with one or more unpaired electrons

– Most elements are paramagnetic

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