prentice hall © 2003chapter 6 chapter 6 electronic structure of atoms chemistry the central science...

Prentice Hall © 2003 Chapter 6

Chapter 6Electronic Structure of Atoms

CHEMISTRY The Central Science

9th Edition


• Electromagnetic Radiation carries energy through space• Speed of EMR through a vacuum: 3.00x108 m/s • wavelike characteristics:

• wavelength, (l distance from crest to crest)• amplitude, A (height)• frequency, n (# of cycles which pass a point in 1 second)

6.1: The Wave Nature of Light


The wave nature is due to periodic oscillations of the intensities of electronic and magnetic forces associated with the radiation

The # of times the cork bobs up and down is the frequency

Frequency and

wavelength are

inversely related

Text, P. 200


• The speed of a wave, c, is given by its frequency multiplied by its wavelength:

• For light, speed = c (that is 3.00 x 108m/s)

c


• Modern atomic theory arose out of studies of the interaction of radiation with matter

• Example: the visible spectrum

The Electromagnetic Spectrum, P. 201

(or Hz)


Text, P. 201


• Sample Problem #7


• Problems with wave theory:– Emission of light from hot objects

• “black body radiation”: stove burner, light bulb filament

– The photoelectric effect– Emission spectra

6.2: Quantized Energy and Photons


• Planck: energy can only be absorbed or released from atoms in certain amounts called quanta

• The relationship between energy and frequency is

where h is Planck’s constant (6.626 10-34 J-s)

hE


Quantization Analogy:Consider walking up a ramp versus walking up stairs:

For the ramp, there is a continuous change in height

Movement up stairs is a quantized change in height


The Photoelectric Effect• Evidence for the particle nature of light -- “quantization”• Light shines on the surface of a metal: electrons are

ejected from the metal• threshold frequency must be reached

• Below this, no electrons are ejected• Above this, the # of electrons ejected depends on the

intensity of the light

Text, P. 204


• Einstein assumed that light traveled in energy packets called photons

• The energy of one photon:

• Energy and frequency are directly proportional

• Therefore radiant

energy must be quantized!

hE


• Sample Problems # 13, 17, 19


Line Spectra• Radiation that spans an array of different wavelengths:

continuous

• White light through a prism: continuous spectrum of colors

• Spectra tube emits light unique to the element in it• Looking at it through a prism, only lines of a few

wavelengths are seen• Black regions correspond to wavelengths that are absent

6.3: Line Spectra and the Bohr Model

Continuous Visible Spectrum, P. 206


Bohr Model• Rutherford model of the atom: electrons orbited the

nucleus like planets around the sun

• Physics: a charged particle moving in a circular path should lose energy

• Therefore the atom should be unstable


3 Postulates for Bohr’s theory:

1. Electrons move in orbits that have defined energies

2. An electron in an orbit has a specific energy

3. Energy is only emitted or absorbed by an electron as it changes from one allowed energy state to another (E=hν)


• Since the energy states are quantized,

the light emitted from excited atoms must be quantized and appear as line spectra

• Bohr showed that

where n is the principal quantum number (i.e., n = 1, 2, 3, … and nothing else)

218 1

J 1018.2n

E


• The first orbit in the Bohr model has n = 1, is closest to the nucleus, and has the lowest energy (ground state)

• The furthest orbit in the Bohr model has n close to infinity


• Electrons in the Bohr model can only move between orbits by absorbing and emitting energy in quanta (hν)

• The amount of energy absorbed or emitted on movement between states is given by

Sample Problems # 21 and 27

hEEE if


Line Spectra, P. 207

The Balmer series for Hydrogen (nf = 2, which is in the visible region)

The Rydberg Equation (P. 206) allows for the calculation of wavelengths for all the spectral lines

n = energy level

n f values fo

r other

regions of the EMS:

Lyman (UV): n f =

1

Paschen (IR): n f =

3

Brackett (IR): n f =

4

Pfund (IR): n f =

5

1722

100974.1111

mRwhere

nnR H

ifH

Note the units

Figure 6.14, P. 208

Using the Rydberg Equation, the existence of spectral lines can be attributed to the quantized jumps of electrons between energy levels (therefore justifying Bohr’s model of the atom)

Balmer Series Energy Level Diagram

Lyman Series

Paschen Series

Sample Problems # 29 and 31


The Electromagnetic Spectrum, P. 201

(or Hz)


Limitations of the Bohr Model• It can only explain the line spectrum of hydrogen

adequately• Electrons are not completely described as small particles• It doesn’t account for the wave properties of electrons

• DEMOS!


• Using Einstein’s and Planck’s equations, de Broglie showed:

• The momentum, mv, is a particle property, but is a wave property

• Sample Exercise 6.5, P. 210

6.4:The Wave Behavior of Matter

mvh


The Uncertainty Principle

• Heisenberg’s Uncertainty Principle: we cannot determine exactly the position, direction of motion, and speed of an electron simultaneously


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

• Solving the equation leads to wave functions (shape of the electronic orbital)

6.5: Quantum Mechanics and Atomic Orbitals

http://en.wikipedia.org/wiki/Schr%C3%B6dinger's_cat


The electron density distribution in the ground state of the hydrogen atom

Text, P. 213


Orbitals and Quantum Numbers• If we solve the Schrödinger equation, we get wave

functions and energies for the wave functions.• We call wave functions orbitals (regions of highly

probable electron location).

• Schrödinger’s equation requires 3 quantum numbers:1. 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 Numbers

• If we solve the Schrödinger equation, we get wave functions and energies for the wave functions• We call wave functions orbitals (regions of highly

probable electron location)

• Schrödinger’s equation requires 3 quantum numbers:1. 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


2. Azimuthal Quantum Number, l

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 (the shape of the orbital) (AKA “subsidiary quantum number”)

3. Magnetic Quantum Number, ml

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


“Aufbau Diagram”: electrons fill low energy orbitals first

Figure 6.17, P. 215

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


• Sample Problems # 41, 43, & 45


The s-Orbitals• All s-orbitals are spherical• As n increases, the s-orbitals get larger

6.6: Representations of Orbitals


the s orbitalsText, P. 216


The p-Orbitals• There are three p-orbitals px, py, and pz

• The three p-orbitals lie along the x-, y- and z- axes of a Cartesian system

• 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


the p orbitalsText, P. 216


The d and f-Orbitals• There are five d and seven f-orbitals

FYI for the d-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

• Text, P. 217

the d orbitals

Text, P. 217


the f orbitals

(not in text)


• http://www.uky.edu/~holler/html/orbitals_2.html

http://www.uky.edu/~holler/html/orbitals_2.html


(-l to +l)Max = (n-1) l letter

(n2)

(# of

orientatio

ns)

Text, P. 214


Orbitals and Their Energies

• Orbitals of the same energy are said to be degenerate• For n 2, the s- and p-orbitals are no longer degenerate

because the electrons interact with each other• Therefore, the Aufbau diagram looks slightly

different for many-electron systems

6.7: Many-Electron Atoms

BOHR

Text, P. 215

MODERN

Text, P. 218

Electron Spin and the Pauli Exclusion Principle

• Since electron spin is also quantized, we define

• ms = spin quantum # = ½

Text, P. 219


• Pauli’s Exclusion 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 capacity of sublevel = 4l + 2• Electron capacity of energy level = 2n2


• Sample Problems # 51 & 55


Hund’s Rule• Electron configurations tell us in which orbitals the

electrons for an element are located• Three rules are applied:

• Aufbau Principle• Pauli’s Exclusion Principle• Hund’s Rule: for degenerate orbitals, electrons fill each

orbital singly before any orbital gets a second electron

6.8: Electron Configurations


Types of electron configurations• Electron configuration notation: energy level, subshell,

# of electrons per orbital• Orbital notation: each ml value is represented by a line,

electrons are also shown• Noble gas configuration: “condensed configuration”

[Proceeding noble gas] electron configuration notation for outer shell electrons

Inner shell e-


• The periodic table can be used as a guide for electron configurations• The period number is the value of n

6.9: Electron Configurations and the Periodic Table

# of columns is related to the number of electrons that can fit

in the subshells

Regular trends

Text, P.

225

Irregularities: half filled and completely filled subshells are

stable

Text, P. 227


• Sample Problems # 59, 61, 63 & 65


End of Chapter 6

prentice hall © 2003chapter 6 chapter 6 electronic structure of atoms chemistry the central science...

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