Atomic Structure and Periodicity

Electromagnetic RadiationThe Nature of Matter

The Atomic Spectrum of HydrogenThe Bohr Model

The Quantum Mechanical ModelQuantum Numbers

Electromagnetic Electromagnetic SpectrumSpectrum

10-12 10-10 10-8

4x10-7 5x10-7 6x10-7 7x10-7

10-4 10-2 1021 104

Electromagnetic Electromagnetic RadiationRadiation

Gamma

X rays

Ultraviolet

Visible (400-700nm)

Infrared

Microwaves

Radio waves

Power waves

Electromagnetic Electromagnetic RadiationRadiation

Three primary characteristics Wavelength (…lambda) Frequency (…nu) Speed (c)

WavelengthWavelength Distance between two consecutive crests

or troughs of a wave

Measured in m or nm, typically

FrequencyFrequency

Number of wave cycles per second that pass a given point in space

Cycle is understood in SI language

Measured in 1/s or s-1, also known as a hertz (Hz)

SpeedSpeed Constant, known as the speed of light

2.9979 x 108m/s

Since the speed of a wave is constant, then frequency and wavelength must vary inversely

c =

Problem #1Problem #1

A wave is known to have a frequency of 5.09 x 1014Hz. What is its wavelength and what type of electromagnetic radiation is it?

Electromagnetic Electromagnetic SpectrumSpectrum

10-12 10-10 10-8

4x10-7 5x10-7 6x10-7 7x10-7

10-4 10-2 1021 104

Problem #1Problem #1

5.89 x 10-7 mVisibleYellow-orange

The Nature of MatterThe Nature of Matter

Matter and energy (in the form of light) were thought to be distinct until 1900 Matter was made of particles that had

mass, took up space, and could absorb or emit any quantity of energy

Light was made of waves that were massless and of unknown location (delocalized)

Max Planck (1858-1947)Max Planck (1858-1947) German physicist

Observed that heated solid bodies emitted energy only in specific whole-number multiples

They were multiples of the quantity “h”

h is known as Planck’s constant and has a value of 6.626 x 10-34J•s

Max Planck (1858-1947)Max Planck (1858-1947) Thus, the change in

internal energy of a system is represented by E = h

“h” came to be known as a quantum

Proved that energy is indeed quantized not continuous

Problem #2Problem #2

Cuprous ions will emit 4.41 x 10-19J when heated to approximately 1200C. What is the wavelength of the light emitted and what color is it?

Electromagnetic Electromagnetic SpectrumSpectrum

10-12 10-10 10-8

4x10-7 5x10-7 6x10-7 7x10-7

10-4 10-2 1021 104

Problem #2Problem #2

4.50 x 10-7 mblue-green

Albert EinsteinAlbert Einstein Proposed the

electromagnetic radiation may be viewed as a stream of particles, known as “photons”

Said that the energy of a photon equaled the change in internal energy that a system experienced

Ephoton= h = hc/

Albert EinsteinAlbert Einstein In 1905, he proposed that

energy has mass and put forth the famed equation

E = mc2 or m = E/c2

Thus,

m = E = hc/ = h c2 c2 c

Established the phrase “dual nature of light”

Prince Louis-Victor Pierre Prince Louis-Victor Pierre Raymond de BroglieRaymond de Broglie

Proved that the opposite of the dual nature of light was true

Showed that particles also exhibited wave properties

de Broglie’s equation replaces the speed of light with the speed of the particle

m = h or = h v mv

                                           

Problem #3Problem #3 Compare the wavelength of an electron

with a mass of 9.11 x 10-31 kg traveling at a speed of1.00 x 107 m/s with that of a tennis ball with amass of 0.0089kg traveling at 42.5 m/s.

Electron—7.27 x 10-11 mTennis ball—1.75 x10-33 m

DiffractionDiffraction Scattering of light from a regular array of

points or lines..make a diffraction pattern

Proves the wave properties of particulate matter

Pattern results from constructive interference Light spots

And destructive interference Dark spots

MatterMatter Exhibits particulate and wave properties

Big bits have tiny wavelengths and have more particulate properties

Itty-bitty bits have larger wavelengths and behave more like waves than particles

Medium bits have fairly equal representation of particles and waves

Atomic Spectrum of Atomic Spectrum of HydrogenHydrogen

When H atoms are excited, they emit the excess energy according to the electromagnetic spectrum

This is known as an emission spectrum

It is not continuous as white light through a prism is

Rather, it is known as a line spectrum

Verifies quantization of energy emission

Line Spectrum of Line Spectrum of HydrogenHydrogen

                                                                                                                                       

      

The Bohr ModelThe Bohr Model developed in 1913 by Danish

physicist, Niels Bohr

Proposed that the electron in H moves in particular circular orbits

Agreed with the emission spectrum of hydrogen assuming the angular momentum of the electron occurred in specific increments

                               

The Bohr ModelThe Bohr Model provides the equation that

gives the energy levels available in hydrogen

E = -2.178 x 10-18 J(Z2/n2) n represents the integer

indicating the distance from the nucleus (will eventually be shown to be the energy level)

Z represents the nuclear charge which is +1 for hydrogen

                               

The Bohr ModelThe Bohr Model If a hydrogen electron is

excited to a higher energy level and then falls back down to the 1st energy level (the ground state), then the associated energy change can be determined.

E = Ef – Ei

                               

E = -2.178 x 10-18 J(1/nf2 – 1/ni

2)

Problem #4Problem #4 Determine the wavelength of light emitted

when a hydrogen electron falls from the 6th energy level to the 1st energy level. What type of electromagnetic radiation is this?

9.38 x 10-8 multraviolet

The Quantum Mechanical The Quantum Mechanical ModelModel

Begun by de Broglie

Remember the dual nature of light and the idea that all matter traveled in waves and as particles?

The Quantum Mechanical The Quantum Mechanical ModelModel

Erwin Schrödinger (1887-1961)

Austrian physicist

Treated electron pathways as standing waves

Designated wave functions (functions of x, y, and z coordinates) that we peons tend to call orbitals

Proved orbitals are not circular

Werner Heisenberg (1901-1976)

German physicist

“We cannot always assign to an electron a position in space at a given time, nor follow it in its orbit, so that we cannot assume that the planetary orbits postulated by Niels Bohr actually exist. Mechanical quantities,

                               

The Quantum Mechanical The Quantum Mechanical ModelModel

such as position, velocity, etc. should be represented, not by ordinary numbers, but by abstract mathematical structures called matrices.“

Proposed the above postulate at the age of 23!!

Later came up with his famed Uncertainty Theory

                               

The Quantum Mechanical The Quantum Mechanical ModelModel

Heisenberg’s Uncertainty Heisenberg’s Uncertainty PrinciplePrinciple

There is a fundamental limitation to just how precisely we can know both the position and momentum of a particle at a given time.

x • (mv) > h/4 x is the uncertainty in position (mv) is the uncertainty in

momentum h is Planck’s constant

                               

ProbabilityProbability

Shown is that of the hydrogen 1s orbital

Distribution graph shows adarker image where an electron tends to be found morefrequently

Approximately 90% of the time, the electron may be found in this sphere

Also called an electron density map

Electron Electron ConfigurationsConfigurations

Energy level

Sublevel

s

p

d

f

# electrons

Electron Electron ConfigurationsConfigurations

Electron Electron ConfigurationsConfigurations

Electron Electron ConfigurationsConfigurations

Orbital DiagramsOrbital Diagrams

E

1s

2s

2px 2py 2pz

3px 3py 3pz

3s

Orbital DiagramsOrbital Diagrams

E

1s

2s

2px 2py 2pz

3px 3py 3pz

3s

Orbital DiagramsOrbital Diagrams

E

1s

2s

2px 2py 2pz

3px 3py 3pz

3s