6.1 the wave nature of light

6.1 THE WAVE NATURE OF

LIGHT

To understand the electronic structure of atoms, one must

understand the nature of electromagnetic radiation

Electromagnetic radiation

•A form of energy exhibiting wave-like behavior as it

travels through space

•Visible light, IR, and X-rays share certain fundamental

characteristics

•All types of electromagnetic radiation move through a

vacuum at a speed of 3.00 × 108 m/s, the speed of light

6.1 THE WAVE NATURE OF LIGHT

Wavelength (), amplitude, and frequency ()•The distance between corresponding points on adjacent waves is

the wavelength

•The number of waves passing a given point per unit of time is the

frequency

Relationship between the wavelength and the frequency

c =

CHARACTERISTICS OF ELECTROMAG-

NETIC WAVES

For waves traveling at the same velocity, the longer the wavelength, the smaller the fre-quency


Different properties of electromagnetic radiation comes

from their different wavelength

THE ELECTROMAGNETIC SPECTRUM


COMMON WAVELENGTH UNITS


SAMPLE EXERCISE 6.1

1. Which wave has the higher frequency?

2. Visible light and IR

3. Blue light and red light

6.2 QUANTIZED ENERGY AND PHO-

TONS

Although the wave model of light explains many aspects

of its behavior, this model cannot explain several phe-

nomena:

•Blackbody radiation

•Photoelectric effect

•Emission spectra

6.2 QUANTIZED ENERGY AND PHO-TONS

As a body is heated, it begins to emit radiation and be-

comes first red, then orange, then yellow, then white as its

temperature increases

HOT OBJECTS AND THE QUANTIZATION OF

ENERGY

The classical theory of radiation

predicts:

Intensity kT/4 Max Planck explained it by as-

suming that energy comes in

packets called quanta E = h

h, Planck’s constant 6.626 10−34 J-s

http://www.goiit.com/posts/downloadAttach/35575.htm

6.2 QUANTIZED ENERGY AND PHO-TONS THE PHOTOELECTRIC EFFECT AND PHO-

TONS Light with a specific frequency or greater causes a metal to emit electrons, but light of lower frequency has no effect

Einstein used Planck’s assumption to explain the photoelec-tric effect.

He concluded that energy is proportional to frequency:

E = h h, Planck’s constant

6.626 10−34 J-s.

6.2 QUANTIZED ENERGY AND PHO-TONS THE PHOTOELECTRIC EFFECT AND PHO-

TONS

6.3 LINE SPECTRA AND THE BOHR MODEL

Radiation composed of a single wavelength is said to be

monochromatic

Most common radiation sources contain

many different wavelength

LINE SPECTRA


LINE SPECTRA

H2 Ne

For atoms and molecules one does not observe a continu-ous spectrum, as one gets from a white light source.

Only a line spectrum of discrete wavelengths is observed.

Rydberg equationRH, Rydberg constant

High voltage under reduced pressure of different gases produces different colors of light


BOHR’S MODEL

The classical “microscopic solar system” model of the atom

cannot explain the line spectrum

Bohr’s postulates

• Electrons in an atom can only occupy certain orbits

(corresponding to certain energies).

• An electrons in a permitted orbit have a specific energy and is in

an “allowed” state. An electron in an allowed energy state will

not radiate energy and therefore will not spiral into the nucleus

• Energy is emitted or absorbed by the electron only as the elec-

tron changes from one allowed energy state to another. This

energy is emitted or absorbed as a photon, E = h

6.3 LINE SPECTRA AND THE BOHR MODEL THE ENERGY STATES OF THE HYDROGEN

ATOM Bohr calculated the energies

corresponding to each al-

lowed orbit for the electron in

the hydrogen atom

RH is the Rydberg constant

n is the principal quantum

number

Ground state & excited state


ATOM

The equation is corresponding to the experimental equation


ATOM


LIMITATIONS OF THE BOHR MODEL

Significance of the Bohr model

•Electrons exist only in certain discrete energy levels, which

are described by quantum numbers

•Energy is involved in moving an electron from one level to

another

The model cannot explain the spectra of other atoms and

why electrons do not fall into the positively charged nucleus

6.4 THE WAVE BEHAVIOR OF MAT-

TER Louis de Broglie suggested:

“If radiant energy could, under appropriate conditions be-

have as though it were a stream of particles, could matter,

under appropriate conditions, possibly show the properties

of a wave?”

An electron moving about the

nucleus of an atom behaves like

a wave and therefore has a

wavelength

de Broglie’s hypothesis is appli-

cable to all matters

6.4 THE WAVE BEHAVIOR OF MAT-

TER

6.4 THE WAVE BEHAVIOR OF MATTER

THE UNCERTAINTY PRINCIPLE Heisenberg showed that the more precisely the mo-

mentum of a particle is known, the less precisely is its position known:

In many cases, our uncertainty of the whereabouts of an electron is greater than the size of the atom itself!

If we have 1% of uncertainty in the speed of electron in hydrogen atom (diameter, 1 × 10-10 m)

6.4 THE WAVE BEHAVIOR OF MATTER

Whenever any measurement is made, some uncertainty exists

This limit is not a restriction on how well instruments can be made; rather, it is inherent in nature

No practical consequences on ordinary-sized objects Enormous implications when dealing with subatomic parti-

cles, such as electrons Short wavelength of light for accuracy in position High energy light will change the electron’s motion There is an uncertainty in simultaneously knowing either

the position or the momentum of the electron that cannot be reduced beyond a certain minimum level

6.5 QUANTUM MECHANICS AND ATOMIC OR-

BITALS Erwin Schrödinger developed a mathematical treatment into which

both the wave and particle nature of matter could be incorporated.

He treated the electron in

a hydrogen atom like the

wave on a guitar string

Overtones vs higher- en-

ergy standing waves

Nodes vs zero amplitude

Solving Schrödinger’s

equation for the hydrogen

atom leads to a series of

mathematical functions –

wave functions

6.5 QUANTUM MECHANICS AND ATOMIC OR-

BITALS These wave functions are repre-

sented by the symbol (psi)

The wave function has no direct

physical meaning

The square of the wave equation,

2, represents the probability that

the electron will be found at that lo-

cation – probability density

This is just a kind of statistical

knowledge – we cannot specify the

exact location of an electron

Figure 6.16 Electron-density distribu-tion

6.5 QUANTUM MECHANICS AND ATOMIC OR-BITALS

ORBITALS AND QUANTUM NUMBERS Solving the wave equation gives a set of wave functions,

or orbitals, and their corresponding energies. Each orbital describes a spatial distribution of electron

density. An orbital is described by a set of three quantum numbers.

PRINCIPAL QUANTUM NUMBER The principal quantum number, n, describes the energy

level on which the orbital resides. The values of n are integers ≥ 1.


ANGULAR MOMENTUM QUANTUM NUMBER

This quantum number defines the shape of the orbital.

Allowed values of l are integers ranging from 0 to n − 1.

We use letter designations to communicate the different

values of l and, therefore, the shapes and types of orbitals.


MAGNETIC QUANTUM NUMBER

The magnetic quantum number describes the three-di-

mensional orientation of the orbital.

Allowed values of ml are integers ranging from −l to l :

−l ≤ ml ≤ l

Therefore, on any given energy level, there can be up to 1

s orbital, 3 p orbitals, 5 d orbitals, 7 f orbitals, etc.


Orbitals with the same value of n form a shell.

Different orbital types within a shell are subshells.

ORBITALS AND QUANTUM NUMBERS



For a one-electron hy-

drogen atom, orbitals

on the same energy

level have the same

energy.

That is, they are de-

generate.

Figure 6.17

6.6 REPRESENTATIONS OF ORBITALS

Spherically symmetric

There is only one s orbital for each value of n (l = 0, ml = 0)

Radial probability function

Nodes

THE S ORBITALS


THE S ORBITALS

Figure 6.21 probability density in the s orbitals of hydrogen.


THE P ORBITALS

The value of l for p orbitals is 1 and the orbital has

three magnetic quantum number ml.

They have two lobes with a node between them.


THE d AND f ORBITALS The value of l for a d orbital is 2 and the orbital has five

magnetic quantum number ml.

Four of the five d orbitals have 4 lobes; the other resem-bles a p orbital with a doughnut around the center.

6.7 MANY-ELECTRON ATOMS

ORBITALS AND THEIR ENERGIES

As the number of electrons

increases, though, so does

the repulsion between them.

In many-electron atoms, or-

bitals on the same energy

level are no longer degener-

ate

For a given value of n, the

energy of an orbital in-

creases with increasing

value of l.

In the 1920s, it was discovered that a beam of neutral

atoms is separated into two groups when passing them

through a nonhomogeneous magnetic field

Electron has two equivalent magnetic field


ELECTRON SPIN

Observation of closely spaced

double lines in spectrum of

many-electron atoms

Electrons have spin.

Spin magnetic quantum num-

ber, ms

The spin quantum number has

only 2 allowed values: +1/2 and

−1/2

No two electrons in the same atom can have identical sets of quantum numbers.

An orbital can hold a maximum of two electrons and they must have opposite spins


PAULI EXCLUSION PRINCIPLE

Electron distribution in orbitals of an atom. The ground state: the most stable electron configuration of

an atom The orbitals are filled in order of increasing energy with no

more than two electrons per orbital Consider the lithium atom

•How many electrons?•Electron configuration?

6.8 ELECTRON CONFIGURATION

paired unpaired

For degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized

- Hund’s rule


HUND’S RULE


HUND’S RULE


(b) How many unpaired electrons exist?


Drawbacks to using x-rays for medical imaging MRI overcomes the drawbacks


TRANSITION METALS The condensed electron configuration includes the elec-

tron configuration of the nearest noble-gas element of lower atomic number

Note that the 19th electron of potassium is occupied in 4s (not 3d)

Transition metals: elements in the d-block of the periodic table

Lanthanides and actinides

6.9 ELECTRON CONFIGURATIONS AND THE PERI-ODIC TABLE

The structure of the periodic table reflects the orbital struc-ture


The periodic table is your best guide to the order in which orbitals are filled

6.1 the wave nature of light

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