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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 Light

The Wave Nature of Light

- All waves have a characteristic wavelength, l,

and amplitude, A. - The frequency, n, 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 nl

c vs. l vs. n

- The longer the wavelength, the fewer cycles are

seen - c l x n
- 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 hn
- h 6.63 x 10-34 J.s (Planck's constant)
- Electromagnetic energy can be transferred in

inter multiples of hn. (2hn, 3hn, ...) - 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 h?.

Quantized Energy and Photons

The 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

Bohrs 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

Bohrs Model of the Hydrogen Atom

Line Spectra

Shows that visible light contains many wavelengths

Bohrs Model of the Hydrogen Atom

Bohrs Model Colors from excited gases arise

because electrons move between energy states in

the atom.

Only a few wavelengths emitted from elements

Bohrs Model of the Hydrogen Atom

Bohrs Model Since 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 gt

1) When n 8, 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 (DE Ef Ei)

could be emitted - I.e.

Bohrs Model of the Hydrogen Atom

Bohrs Model We can show that ?E (-2.18 x

10-18 J)(1/nf2 - 1/ni2 ) When ni gt nf, energy

is emitted. When nf gt 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 (n4) to

the second energy level n2. - Indicate whether energy is absorbed or emitted as

the electron moves from n4 to n2. 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 n5 to n2. 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 Einsteins and Plancks equations, de

Broglie supposed

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.

The Uncertainty Principle

Heisenbergs 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.

Quantum Mechanics and Atomic Orbitals

- 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.

Quantum Mechanics and Atomic Orbitals

Quantum Mechanics and Atomic Orbitals

If we solve the Schrödinger equation, we get

wave functions and energies for the wave

functions. We call wave functions

orbitals. Schrödingers equation requires 3

quantum numbers Principal Quantum Number, n.

This is the same as Bohrs n. As n becomes

larger, the atom becomes larger and the electron

is further from the nucleus.

Orbitals and Quantum Numbers Azimuthal 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. Magnetic quantum numbers give the 3D

orientation of each orbital.

Orbitals and Quantum Numbers

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)

Quantum Mechanics and Atomic Orbitals

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.

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Representation of Orbitals

The s 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 Orbitals

The s Orbitals

Representation of Orbitals

The p 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.

Representation of Orbitals

The p Orbitals

Representation of Orbitals

The d and f 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 Orbitals

The d Orbitals

Orbitals 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

Orbitals in Many Electron Atoms

Energies of Orbitals

Orbitals in Many Electron Atoms

- Electron 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.

Orbitals in Many Electron Atoms

Electron Spin and the Pauli Exclusion Principle

Orbitals in Many Electron Atoms

Electron Spin and the Pauli Exclusion Principle

Since electron spin is quantized, we define ms

spin quantum number ? ½. Paulis 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

- 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 (Hunds rule).

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

- 1s2

2s2

2p6

3s2

3p6

4s2

3d10

4p6

5s2

4d10

5p6

6s2

- 12

- 56

- electrons

- 4

- 20

- 38

- 2

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Electron Configurations and the Periodic Table

Electron Configurations and the Periodic Table

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 Ne3s23p3.

Exceptions

- Ti Ar 4s2 3d2
- V Ar 4s2 3d3
- Cr Ar 4s1 3d5
- Mn Ar 4s2 3d5
- Half filled orbitals.
- Scientists arent 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