Ch 5 Quantum Theory

7/28/2019 Ch 5 Quantum Theory

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Quantum Theory and theElectronic Structure of Atoms


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Atom interact through their outer parts, their

electrons.

The arrangement of electrons in atoms are

referred to as their electronic structure.

Electron structure relates to:

Number of electrons an atom possess.

Where they are located.

What energies they possess.

Electronic Structure


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Properties of Waves

Wavelength(l) is the distance between identical

points on successive waves.

Ampl i tudeis the vertical distance from themidline of a wave to the peak or trough.

Frequency(n) is the number of waves that pass

through a particular point in 1 second (Hz = 1cycle/s).

The speed (u) of the wave = l x n


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Identifying l and n


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The Electromagnetic Spectrum


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l

n

7

l x n = cl = c/nl = 3.00 x 108 m/s/ 6.0 x 104 Hz

l = 5.0 x 103 m

A photon has a frequency

of 6.0 x 104 Hz. Convertthis frequency into

wavelength (nm). Does

this frequency fall in the

visible region?

l = 5.0 x 1012 nm


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The yellow light given off by a sodium vapor

lamp used for public lighting has a wavelength of

589 nm. What is the frequency of this radiation?

Class Guided Practice Problem

ln=c A laser used to weld detached retinas produces

radiation with a frequency of 4.69 x 1014 s-1.What is the wavelength of this radiation?


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Planck: energy can only be absorbed or

released from atoms in certain amounts chunks

called quanta.

The relationship between energy and frequency

is

where his Plancks constant (6.626 10-34 J.s).

.

Quantized Energy and Photons

nhE=


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Plancks theory revolutionized experimental

observations.

Einstein:

Used plancks theory to explain the photoelectric

effect.

Assumed that light traveled in energy packets

called photons. The energy of one photon:

The Photoelectric Effect

nhE=


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Light has both:

1. wave nature

2. particle nature

hn = KE + W

Mystery #2, Photoelectric Effect

Solved by Einstein in 1905

Photonis a particle of light

KE = hn - W

hn

KE e-

where Wis the work function and

depends how strongly electrons

are held in the metal


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E= h x n

E= 6.63 x 10-34 (Js) x 3.00 x 10 8 (m/s) / 0.154 x 10-9 (m)

E= 1.29 x 10 -15 J

E= h x c / l

When copper is bombarded with high-energy

electrons, X rays are emitted. Calculate the energy(in joules) associated with the photons if the

wavelength of the X rays is 0.154 nm.


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Calculate the energy of a photon of yellow light

whose wavelength is 589 nm.


nhE= (a)Calculate the smallest increment of energy (a

quantum) that can be emitted or absorbed at a

wavelength of 803 nm. (b) Calculate the energyof a photon of frequency 7.9 x 1014 s-1. (c) What

frequency of radiation has photons of energy

1.88 x 10-18 J? Now calculate the wavelength.


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Line Spectra Radiation composed of only one wavelength is

called monochromatic.

Most common radiation sources that produce

radiation containing many different wavelengths

components, a spectrum.

This rainbow of colors, containing light of all

wavelengths, is called a continuous spectrum. Note that there are no dark spots on the

continuous spectrum that would correspond to

different lines.

Line Spectra and the Bohr Model


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Line Emission Spectrum of Hydrogen Atoms


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Specific Wavelength Line Spectra

When gases are placed under reduced pressure in a tube and

a high voltage is applied, radiation at different wavelengths

(colors) will be emitted.


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Rutherford assumed the electrons orbited thenucleus analogous to planets around the sun.

However, a charged particle moving in a circular

path should lose energy.

This means that the atom should be unstable

according to Rutherfords theory.

Bohr noted the line spectra of certain elements

and assumed the electrons were confined to

specific energy states. These were called orbits.

Bohr Model


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1. e- can only have

specific (quantized)

energy values

2. light is emitted as e-

moves from one energy

level to a lower energylevel

Bohrs Model of the

Atom (1913)


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Colors from excited gases arise because electrons

move between energy states in the atom.

Line Spectra (Colors)


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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

where n is the principal quantum number (i.e., n =

1, 2, 3, and nothing else).

Line Spectra (Energy)

=

2

18 1J1018.2

n

E


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De Broglie (1924) reasoned

that e- is both particle andwave.

u = velocity of e-

m = mass of e-

2pr= nl l = hmu


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Chemistry in Action: Electron Microscopy

STM image of iron atoms

on copper surface

le = 0.004 nm

Electron micrograph of a normal

red blood cell and a sickled red

blood cell from the same person


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Schrdingerproposed 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


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Electron Density Distribution

Probability of finding an electron in a hydrogen

atom in its ground state.


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1. Principal Quantum Number, n

the same as Bohrs n. As n becomeslarger, the atom becomes larger and

the electron is further from the nucleus.

(n= 1, 2, 3)

Schrdingers Three Quantum

Numbers


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2. Azimuthal Quantum Number, l

quantum number depends on the

value of n. values oflbegin at 0 and increase to

(n - 1). We usually use letters forl(s,

p, dand fforl= 0, 1, 2, and 3).

Usually we refer to the s,p, dand f-

orbitals. (l= 0, 1, 2n-1).

defines the shape of the orbitals.


Numbers


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3. Magnetic Quantum Number, ml

quantum number depends on l.

magnetic quantum number has integral

values between -land +l.

Magnetic quantum numbers give the3D orientation of each orbital in

space. (m = -l0+1)


Numbers


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Orbitals and Quantum Numbers


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(a) For n = 4, what are the possible values ofl?

(b) Forl= 2. What are the possible values of

ml

? What are the representative orbital for the

value oflin (a)?

(c) How many possible values forland mlarethere when (d) n = 3; (b) n = 5?


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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).

Representations of Orbitals

The s-Orbitals


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The s-Orbitals


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There are threep-orbitalspx,py, andpz.

The threep-orbitals lie along thex-, y- and z-

axes of a Cartesian system.

The letters correspond to allowed values ofmlof

-1, 0, and +1.

The orbitals are dumbbell shaped.

As n increases, thep-orbitals get larger.

Allp-orbitals have a node at the nucleus.

The p-Orbitals


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The p-Orbitals

Electron-distribution of a 2p

orbital.


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There are five dand seven f-orbitals.

Three of the d-orbitals lie in a plane bisecting

thex-, y- and z-axes.

Two of the d-orbitals lie in a plane aligned along

thex-, y- and z-axes.

Four of the d-orbitals have four lobes each.

One d-orbital has two lobes and a collar.

The d and f-Orbitals


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Orbitals can be ranked in terms of energy to

yield an Aufbau diagram.

As n increases, note that the spacing between

energy levels becomes smaller.

Orbitals of the same energy are said to bedegenerate.

Orbitals and Quantum Numbers


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Orbitals and Their Energies


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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 Principle


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Exclusion Principle


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Paramagneticunpaired electrons

2p

Diamagneticall electrons paired

2p


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Since electron spin is quantized, we define ms=

spin quantum number = .

Paulis Exclusions Principle: no two electrons

can have the same set of 4 quantum numbers.

Therefore, two electrons in the same orbitalmust have opposite spins.


Exclusion Principle


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Electron configurations tells us in which

orbitals the electrons for an element are located.

Three rules:

electrons fill orbitals starting with lowest nand

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).

Electron Configurations: Hunds Rule


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Electron con f igurat ionis how

the electrons are distributed

among the various atomic orbitalsin an atom.

1s1

principal quantum

numbern

angular momentum

quantum numberl

number of electrons

in the orbital or subshell

Orbital diagram

H

1s1

Order of orbitals (filling) in multi-electron atom


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Order of orbitals (filling) in multi-electron atom

1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s


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What is the electron configuration of Mg?

Mg 12 electrons

1s < 2s < 2p < 3s < 3p < 4s

1s22s22p63s2 2 + 2 + 6 + 2 = 12 electrons

Abbreviated as [Ne]3s

2

[Ne] 1s

2

2s

2

2p

6

What are the possible quantum numbers for the last

(outermost) electron in Cl?

Cl 17 electrons 1s < 2s < 2p < 3s < 3p < 4s

1s22s22p63s23p5 2 + 2 + 6 + 2 + 5 = 17 electrons

Last electron added to 3p orbital

n = 3 l= 1 ml= -1, 0, or +1 ms = or -


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The periodic table can be used as a guide for

electron configurations.

The period number is the value ofn. Groups 1A and 2A (1 & 2) have the s-orbital

filled.

Groups 3A - 8A (13 - 18) have thep-orbital filled. Groups 3B - 2B (3 - 12) have the d-orbital filled.

The lanthanides and actinides have the f-orbital

filled.

Electron Configurations and the

Periodic Table

Outermost subshell being filled with electrons


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Outermost subshell being filled with electrons


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Write the electron configurations for the

following atoms: (a) Cs and (b) Ni

Write the electron configurations for the

following atoms: (a) Se and (b) Pb


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After Ar the dorbitals begin to fill.

After the 3dorbitals are full, the 4p

orbitals begins to fill. Transition metals: elements in

which the delectrons are the

valence electrons.

Transition Metals


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From Cs onwards the 4forbitals begin to fill.

Note: La: [Xe]6s25d14f0

Elements Ce - Lu have the 4forbitals filled and are

called lanthanides orrare earth elements. Elements Th - Lr have the 5forbitals filled and are

called actinides.

Most actinides are not found in nature.

Lanthanides and Actinides


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Class Practice

53

Make condensed electronic configuration

for all Representative elements


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Paramagnetic

unpaired electrons

2p

Diamagnetic

all electrons paired

2p

Ch 5 Quantum Theory

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