Lecture notes: CHEM103 Spring 2008 – September 30, 2008

GOAL:  UNDERSTAND THE NATURE OF ELECTRONS

HOW?  BY THE UNDERSTANDING THE INTERACTIONS OF LIGHT WITH MATTER

OBJECTIVES FOR TODAY:

0)    NOTE ABOUT LAB THIS WEEK!

1)    REVIEW: particle-wave duality

a.     light as a wave, including proof

2)    Light as a particle

a.     Maxwell Planck & blackbody radiation: quantum mechanics

b.     Line spectra of gases and in the sun

c.     Proof of particle nature from Einstein

3)    Bohr & “solar system” model of the atom

4)    Electrons ALSO behave as waves (duality): MORE quantum mechanics

5) everything PARTICLE as WAVES: the DeBroglie equation: EVEN MORE quantum mechanics

6) emission and absorption of light by atoms: INTERACTION OF LIGHT W/ MATTER

7) calculating electron energy changes in atomic transitions USING Planck & Rydberg

The nature of light: particle-wave duality

1)  light can be described as a WAVE: using the concepts of wavelength & frequency

Proof that light behaves as a wave:

Examples:   diffraction

interference

now: combine diffraction & interference (2 slit experiment)

INTERACTIONS BETWEEN LIGHT AND MATTER, continued…

2) light can be described as a PARTICLE – can be counted individually:

NOW:  “CLASSICAL MECHANICS VS. QUANTUM MECHANICS”

Planck’s idea…

you can’t break up energy into inifinitely small bits, but must take it in pieces.

(Analogy: gaining potential energy (height) by climbing the stairs, instead of walking up a ramp.)

Eradiation = n × h × n

h = 6.626×10-34 J·sec   (Planck’s constant)

“nu” = frequency   (Hz or seconds-1)

(AND n = 0, 1, 2, 3… the number of steps OR “QUANTA”)

SO: h×n describes the energy of ONE photon  (Planck’s constant  x  photon frequency)

…and we can write:

Ephoton = h × n

Calculate the amount of energy in a photon with a wavelength of 500 nm:

…with a wavelength of 12 mm:

c = l × n    (speed = wavelength  x  frequency)

Ephoton = h × n

combine these…

LINE SPECTRA (EMITTED AND ABSORBED)

note: this is very different than “blackbody radiation”

Emission lines for different materials

Hydrogen:

Helium:

Neon:

Sodium:

Different colors = different wavelengths;

Different wavelengths = different frequencies

Different frequencies = different energies, but only at specific values!

“Frauenhofer lines” in the solar spectrum

What does this mean?

Light is being absorbed at specific energies.

Conservation of energy tells us the energy must go somewhere!

WHERE?   Into the atoms; but specifically into the electrons – SO THESE INTERACT!

Remember: from this point forward, it is the electrons that define chemical properties!

AND, for electrons, location doesn’t matter – ENERGY is everything!

FINALLY: PROOF THAT THIS SOLUTION REALLY WORKS!

Albert Einstein’s interpretation of the photoelectron effect (1905)

KEY IDEA: NUMBER OF PHOTONS (INTENSITY) IS LESS IMPORTANT THAN ENERGY OF PHOTONS (FREQUENCY);

ONCE THRESHOLD FREQUENCY IS EXCEEDED, THEN INTENSITY MATTERS

SO WE GO BACK TO THE ATOM & ELECTRONIC “STRUCTURE”

Neils Bohr and the Hydrogen Atoms  (1911)

(a postdoctoral student of JJ Thomson AND Rutherford)

THEORY:   Electrons “orbit” the nucleus much like planets orbit the sun – but the attraction different!

(Why is this a problem?)

THE SOLUTION: just like light,

the orbital velocities (angular momentum) of these electron orbits are QUANTIZED!

(ONLY CERTAIN SOLUTIONS TO THE PROBLEM ALLOWED!)

BUT THIS ONLY WORKS IF ELECTRONS ARE A WAVE, JUST LIKE LIGHT…

How this helps with Bohr’s quantum electron orbits – a way to think about it…