Atomic Structure IIt’s not about Dalton

anymore…

http://plus.maths.org/latestnews/may-aug07/strings/atoms.jpg

First…

• To understand the electronic structure of the atom we need to review the properties of electromagnetic radiation.

Figure 7.1

Frequency and

Wavelength

c = wavelength

frequency

C = speed of light

The Wave The Wave Nature Nature of Lightof Light

Amplitude (intensity) of a wave.

The waveheight or amplitude determines radiation intensity. The wavelength is related to the energy of the radiation.

λ, ν, and Energy

• As λ decreases and ν increases, what happened to the energy of the radiation?

where h = Planck’s constant

(6.626 × 10-34 m2 kg/s)

h cE = h =

Regions of the electromagnetic spectrum.

The infinite number of wavelengths of electromagnetic radiation have been classified into groups as shown below.

SOLUTION:

Interconverting Wavelength and Frequency

Use c =

10-2

m1 cm

10-9

m1 nm

= 1.00x10-10 m

= 325x10-2 m

= 473x10-9

m

=3x108

m/s1.00x10-10

m

= 3x1018 s-

1

=

=

3x108

m/s325x10-2 m= 9.23x107 s-

1

3x108

m/s473x10-9 m= 6.34x1014

s-1

PROBLEM: A dental hygienist uses x-rays (= 1.00A) to take a series of dental radiographs while the patient listens to a radio station ( = 325 cm) and looks out the window at the blue sky (= 473 nm). What is the frequency (in s-1) of the electromagnetic radiation from each source? (Assume that the radiation travels at the speed of light, 3.00x108 m/s.)

o

325 cm

473nm

1.00Ao 10-10 m

1Ao

SOLUTION:

Calculating the Energy of Radiation from Its Wavelength

PROBLEM: A cook uses a microwave oven to heat a meal. The wavelength of the radiation is 1.20cm. What is the energy of one photon of this microwave radiation?

After converting cm to m, we can use the energy equation, E = h combined with = c/ to find the energy.

E = hc/

E =6.626X10-34J*s 3x108m/

s1.20cm

10-

2mcm

x= 1.66x10-23J

Particle or Wave?

Different behaviors of waves and particles.

The diffraction pattern caused by light passing through two adjacent slits.

Light is a wave…right?

• Light falling on alkali metals causes electrons to be released from the metal.

• The # of electrons depends on the intensity of light.

• There are specific wavelengths of light that cause the release of e-.

• This is called the photoelectric effect.

Light is a wave…right?

• Einstein’s interpretation of the photoelectric effect (1905) was that light is quantized in packets of set energy called photons. (He won the Nobel Prize for this.)

• This meant that light had characteristics of particles!

Electrons are particles…right?

• In 1925, de Broglie stated that all particles have a wavelength described by the equation:

λ = h/p where p= momentum• Electrons show diffraction pattern

when passing through a slit• So light and particles have a dual nature.

Back to atomic structure…

• We already know an atom contains a nucleus with p+ and no. Electrons orbit the nucleus.

• It was known that atoms emit a unique spectrum of lines when excited. Rydberg derived an equation that related the lines.

• R is the Rydberg constant = 1.096776x107 m-1

= RRydberg equation -1

1

n22

1

n12

Flame test colors derive from electrons changing energy levels.

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/atspect2.html

Atomic emission spectra

Clockwise from lower left:neon, helium, hydrogen,mercury, nitrogen

Spectra Site

• http://jersey.uoregon.edu/vlab/elements/Elements.html

Absorption and emission spectra for element arranged on the periodic table

Back to atomic structure…

• Bohr theorized that the emission spectra of atoms described by Rydberg’s equation were caused by the transition of electrons between specific energy levels (orbits).

• http://www.upscale.utoronto.ca/GeneralInterest/Harrison/BohrModel/Flash/BohrModel.html

Electron locations

• When an electron occupies its usual energy level it is in the ground state.

• When an electron absorbs a photon and moves to a higher energy level it is in an excited state.

• The energy levels are “quantized”. Atoms can only transition between set levels.

• Why are the levels set where they are?

More on electrons as waves

• Since electrons have wave motion Schrödinger applied the classic wave equations to the motion of a hydrogen electron. Certain wavelengths reinforced each other and were allowed.

• This generated regions occupied by an electron of set energy termed orbitals.

Wave motion in restricted systems.

More on electrons as waves

• Heisenberg stated that in measuring the electron there is uncertainty so we can only calculate a probable location for the electron. This is called the Heisenberg Uncertainty Principle.

Electron probability in the ground-state H atom.

The 2p orbitals.

The 3d orbitals.

F orbitals

CLASSICAL CLASSICAL THEORYTHEORYMatter

particulate,

massive

Energy continuou

s, wavelike

Since matter is discontinuous and particulate perhaps energy is discontinuous

and particulate.Observation

Theory

Planck: Energy is quantized; only certain values allowed

blackbody radiation

Einstein: Light has particulate behavior (photons)

photoelectric effect

Bohr: Energy of atoms is quantized; photon emitted when electron changes orbit.

atomic line spectra

Summary of the major observations and theories leading from classical theory to quantum theory.

Since energy is wavelike perhaps matter is wavelike

Observation

Theory

deBroglie: All matter travels in waves; energy of atom is quantized due to wave motion of electrons

Davisson/Germer: electron diffraction by metal crystalSince matter has mass perhaps energy has

massObservation

Theory

Einstein/deBroglie: Mass and energy are equivalent; particles have wavelength and photons have momentum.

Compton: photon wavelength increases (momentum decreases) after colliding with electron

QUANTUM THEORY

Energy same as Matterparticulate, massive, wavelike