Lecture notes: CHEM103 Spring 2008 – October 2, 2008

OBJECTIVES FOR TODAY:

0)    REVIEW: quantized electron orbits

1)    DeBroglie and wave-particle duality of all matter

a.     …including electrons – this explains the quantized orbits

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

a.     calculating electron energy changes in atomic transitions using Planck AND Rydberg equations

b.     absorption of energy

c.     emission of energy

d.     ground state

e.     ionization energy

3)    electrons as a 3-D wave

a.     uncertainty principle: probability NOT location!

b.     Schrodinger’s equation – yikes!

c.     orbital shapes (waveforms) of electrons

d.     describing them with 4 quantum numbers

THE PROBLEM: electrons in orbits around a central nucleus

interactions between charges should cause the electron to spiral into the nucleus - NOT GOOD!!!

THE SOLUTION: just like light,

the orbital velocity or radius (energy) 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

This is first theorized by Prince Louis-Victor Pierre Raymond de Broglie -- the wave nature of all matter!

For ALL objects – we are all quantized!!!    (Yep – another Nobel prize!)

REVIEW:

Einstein:   E = mc2

Planck:     E = hc/l

DeBroglie:         l = h/mv            à               The electron has a wavelength!

(mass must be in kg because “h” has units of J*s, and 1 J = kgm2/s2)

Example: a baseball has a wavelength determined by…

5.00 oz @ 100.0 mph

mb = 5 oz  (16 oz/lb; 453.6 g/lb)  =  0.142 kg

vb = 100 mi/hr  (5280 ft/mi; 12 in/ft; 2.54 cm/in; 3600 s/hr)  =  44.70 m/s

Calculate:  wavelength of an electron

h = 6.626 x 10-34 J·s

me = 9.109 x 10-31 kg

ve = 2.19 x 106 m/sec

= 3.32 x 10-10 m

(Diameter of a hydrogen atom: ~ 1 Å – or 10-10 m)

Finally: proof that electrons can behave as a wave:

Remember J.J. Thompson? The father theorized that electrons are particles;

His son showed that they are waves…

(G.P. Thomson shows that electrons experience “diffraction”, just like light by doing a 2-slit experiment)

I.                 Conclusion: electrons can behave as a wave.

If they can behave like a wave (like light) then their energy may be “quantized” (M. Planck).

NOT all orbits are allowed; only certain energies or “energy levels” (N. Bohr) .

II.             Remember, CONSERVATION of energy

“moving” electrons from one quantized “orbit” to another requires (or releases) energy!

Conclusion: in other words, everytime an electron changes a (quantized) level,

ONE photon is created OR destroyed to balance out the energy change!

DEFINE:  Absorption vs. Emission

Different representations of energy level diagrams:

VS.

NOTES:

Energy increases as you go up in the energy level diagram

Energy at top (at infinite distance from the nucleus) is equal to 0

(what does this mean? “Ionization”)

HOW IS THIS POSSIBLE?

All values of energy levels are NEGATIVE in sign

ANALOGY: atom at the bottom of a deep “potential” well…

Example: spectrum of the hydrogen atom

NOW CALCULATE USING THESE TO DETERMINE ENERGY, WAVELENGTH, FREQUENCY

EXAMPLE 1: Find wavelenth of transition from n = 5 to n = 3 using Planck’s equation.

Planck’s equation:  DE = hc/l          DE = E final -- E initial

(note: difference between E and DE!)

EXAMPLE 2:  NOW, find same wavelenth using the Rydberg equation

Rydberg equation:

(where R = Rydberg constant) = 1.09737316 x 107 m-1

Note - we can combine the Rydberg equation:

with…

Planck’s equation:       ΔE = hc/λ

CONCLUSIONS: BOTH RYDBERG EQUATION AND PLANCK’S EQUATION GIVE THE SAME RESULT!

BUT: Rydberg uses integers and works ONLY for H

Planck’s equation with DE = E fin – E init ( and DE = hn) works for all atoms, if E levels known

This IS extraordinary!  Planck set out to explain a totally different problem and ended up explaining Rydberg’s spectra.

NOW – WE WANT TO KNOW MORE ABOUT WHAT THESE “ORBITS” LOOK LIKE:

HEISENBERG’S UNCERTAINTY PRINCIPLE

can’t simultaneously know both:

1)    Energy (momentum) of electron

2)    Position of electron (in space around the atom)

Conclusion: only determine PROBABILITY of location of electron in space