The Electromagnetic Spectrum and the Model of the Atom

Part I

Chemistry – Mrs. Cameron

The Purpose of Science

The purpose of science to make

models that explain natural phenomena.

Scientific ModelsA model is the best possible explanation

which accounts for all observed phenomenon and has predictability.

1) An unanswered question means change the model.

2) Predictability is the test of a good or “true” model.

Radioactivity and Light have been tools to discover the structure of

atoms.

• Do you Remember?– Thompson’s Cathode Ray Experiment– Rutherford’s Gold foil Experiment

Thomson’s Plum-Pudding Model

Ernest Rutherford’s Gold Foil Experiment

• Results of the Rutherford experiment

(a) The results that the metal foil experiment would have yielded if theplum pudding model had been correct

(b) Actual results

Rutherford’s Nuclear Model of the atom

•Small, dense, positively charged nucleus

•Contains protons (+1 charge)

•Contains neutrons (no charge)

•Remainder of the atom is mostly empty space

•Contains electrons (-1 charge) in the “empty space”

• Let’s Talk about LIGHT

New Evidence: Continuous and Line Spectra

White Light

• Given off by objects heated to a very high temperature.

• When an object is heated, it first gives off a red glow then, as more energy is added it begins to glow “white hot.”

When white light is passed through a prism, the light refracts, or bends to display all of its component colors

The Wave Nature of Light

• All waves exhibit similar characteristics and properties:

Crest – the top of a wave

Trough – the bottom of the wave

(on next slide)

Origin – the center line through which the wave oscillates

Wave crest or peak

The Wave Nature of Light

Origin

Amplitude – distance from the origin to the crest or the origin to the trough of a wave. (Indicates intensity)

Frequency () – the number of waves that pass a given point in a given amount of time

Wavelength (λ) - distance from crest to crest or trough to trough

Speed (Velocity) – the amount of distance covered in a specified amount of time.

←trough

Crest

The Wave Nature of Light

Wave Behaviors

• Reflection – a wave strikes an object and bounces off

• Refraction – the bending of waves• Diffraction – the bending of waves around

an opening or around the edge of an object

• Interference – the ability of two or more waves to add together forming regions of large or small amplitude.

Wave Interference patterns

19

Light Exhibits Interference

• Constructive interference: waves “in-phase” create waves of greater amplitude ( they add)

• Destructive interference: waves “out-of-phase” create waves of lower amplitude (they cancel out)

The Electromagnetic Spectrum

• Visible light is one type of electromagnetic radiation.

• The arrangement of electromagnetic waves by their wavelength is called the electromagnetic spectrum

• The spectrum ranges from high energy, shorter wavelengths of radiation to long wavelength, lower energy radiation.

• The visible portion of the spectrum is very small.

The Wave Nature of Light

Ionizing RadiationIonizing Radiation Nonionizing Radiationonizing Radiation

X-rays

Units for Wave Characteristics

• Wavelength (λ “lambda”) = meters with a Greek prefix (nanometers , nm)

• Frequency ( “nu”) –cycles per second or Hertz

(1/s, sec-1, Hz)

• Speed – meters per second

(m/s)

Wave Calculations– All electromagnetic radiation travels at the same

speed through the vacuum of space:– 3.00 x 108 m/s (c)

– Wavelength and frequency are inversely proportional: λ = c/

– Energy and frequency are directly proportional:

E = h

E = energy in joules,

h = Plank’s constant 6.626 10-34 J·s

The Dual Nature of Light

Light behaves as both a wave and as a particle.

Evidence:

1) The glowing of heated metals

(first infra red, then visible as Tº)

2) The photoelectric effect

The Work of Max Planck(1858-1947)

• Able to predict the wavelengths of light changes with temperature

• Energy must be emitted in a “Quantized” way, or restricted to certain quantities.

• “Quantum” (singular) or “Quanta” (Plural)• A quantum is a packet of energy

• VERY SMALL• Related through Planck’s Constant• h= 6.626 10-34 J·s, E = h

The Photoelectric Effect

• When light is shined on a piece of metal, electrons are ejected from the metal

• Only light containing enough energy (of a certain wavelength and frequency) works

The Photoelectric Effect

Einstein and the Photoelectric effect

• Albert Einstein (1879-1955) proposes that light has a particle nature too.

• He relates Planck’s idea of “quantized energy” to light.

• Light energy quanta = photons

• Photons transfer energy to electrons when light strikes the metal.

• Photons must be of sufficient energy for this to occur.

What do you see?

Depending on how you look at this it can be an old lady or a young lady turning her head.

The picture has a dual nature

Line Spectra of Elements

• A line spectrum is a spectrum that contains only certain colors, or wavelengths of light.

• The rainbow is a continuous spectrum

• Elements emit line spectra when they are vaporized in an intense flame or with electricity.

Continuous spectrum of white light

Line spectra of elements

Line Spectra and the Quantization of Energy

Neils Bohr (1885-1962)Planetary Model of the Atom

• Combines Rutherford’s nuclear model and Planck’s quanta of energy.

• Electrons must have certain energy levels in which they travel. (Energy Level Postulate)

• Energy of Electrons must be quantized to explain line spectra.

(Transitions Between Energy Levels)

Bohr Model

Ground state = energy level closest to the nucleus

Excited state = energy levels farther away from the nucleus

Energy levels represented by quantum numbers ex. n = 1, n= 2, n = 3 etc.

Emission Spectrum of Hydrogen

http://upload.wikimedia.org/wikipedia/commons/4/4c/Emission_spectrum-H.png

• In general, the line spectrum of an element is

rather complicated

• The line spectrum of hydrogen, with a single electron,

is the simplest

• Atomic line spectra tell us that when an excited atom loses energy, not just any arbitrary amount can be lost

• This is possible if the electron is restricted to certain energy levels

• The energy of the electron is said to be quantized

The Evidence of Line Sprectra:

Emission of Light During Movement of Electrons

http://iws.collin.edu/biopage/faculty/mcculloch/1406/outlines/chapter%2010/Ma10-8b.JPG

• J.J. Balmer equation for visible spectrum of Hydrogen

v = 1/ = 1.097 x 107/m (1/n12 - 1/n2

2)

Which led to…..

• The Rydberg equation can be used to calculate all the spectral lines of hydrogen

Rydberg Equation

•Used to calculate the wavelengths of all the spectral lines of hydrogen.

•Atomic spectra indicate that when an excited atom loses energy, the energy is in discrete amounts - or “quantized.”

•n1 and n2 are positive integers

= Rydberg constant = 109,678 cm-1

• Bohr proposed that the electrons moved around the nucleus is fixed paths or orbits much like the planets move around the sun

• The orbits, labeled with the integer n, have energy

•

• This equation allows the calculation of the energy of any orbit

2f

2i

Hif

11ν

nnRhEEE

Bohr was able to use this model to calculate the energies of the light given off by the hydrogen.

E = h

Unfortunately, the model became too mathematically complicated for any element with more electrons than hydrogen.

Also, electrons not completely explained as particles

Limitations of the Bohr Model

•It cannot explain the spectra of atoms other than hydrogen.

•Electrons do not move about the nucleus in circular orbits.

•However - the model introduces two important ideas:

•The energy of an electron is quantized: electrons exist only in certain energy levels described by quantum numbers.

•Energy gain or loss is involved in moving an electron from one energy level to another.

Matter Waves

• Louis DeBroglie (1892-1897)– Electrons (matter) have a dual nature just like

light.– Proved it mathematically

– Evidence: diffraction patterns produced by beams of electrons

http://www.microscopy.ethz.ch/TEM_ED_examples.htm

Electron Diffraction Patterns

E = mc2 and E = h

λ = c/ (solve for ) = c/ λ (Replace with c/ λ) E = h c/ λ

(Both sides of the equation equal “E” so you can equate one to the other)

hc/ λ = mc2

(solve for λ)

λ = hc = h

mc2 mc

(replace the speed of light with the speed of the particle)

λ = h

ms

You can calculate the wavelength of any object!

Matter Wave Equations:

λ = h ms

Why do we not see these waves?

Because for relatively large objects their mass is too large and their speed too slow for the wavelengths to be observed.

Remember, h = 6.626 x 10-34 J · s

Electrons: - small mass (9.109 x 10-28 g) - travel REALLY fastso we can observe the wave behaviors

To be Continued………