1. Atomic Structure
Figure 6.27

2. The Wave Nature of Light
All waves have a characteristic wavelength, l, and amplitude, A.
Frequency, n, of a wave is the number of cycles which pass a point in one second.
Speed of a wave, c, is given by its frequency multiplied by its wavelength:
For light, speed = c = 3.00x108 m s-1 .
The speed of light is constant!

3. The Wave Nature of Light

4. The Wave Nature of Light

5. The Wave Nature of Light

6. X – rays
Microwaves
Comment(s)
Wavelength: λ (m)
1.00x10-10 m
1.00x10-2 m
Frequency: ν (s-1)
Energy: E (J)

8. Quantized Energy and Photons
Planck: energy can only be absorbed or released from atoms in certain amounts called quanta.
The relationship between energy and frequency is
where h is Planck’s constant (  J s ) .

9. Quantized Energy and Photons
The Photoelectric Effect and Photons
Einstein assumed that light traveled in energy packets called photons.
The energy of one photon is:

10. Nature of Waves: Quantized Energy and Photons
X – rays
Microwaves
Comment(s)
Wavelength: λ (m)
1.00x10-10 m
1.00x10-2 m
Frequency: ν (s-1)
Energy: E (J)

11. Line Spectra and the Bohr Model
Radiation composed of only one wavelength is called monochromatic.
Radiation that spans a whole array of different wavelengths is called continuous.
White light can be separated into a continuous spectrum of colors.
Note that there are no dark spots on the continuous spectrum that would correspond to different lines.

13. Line Spectra and the Bohr Model
Colors from excited gases arise because electrons move between energy states in the atom. (Electronic Transition)

15. Line Spectra and the Bohr Model
Since the energy states are quantized, the light emitted from excited atoms must be quantized and appear as line spectra.
After lots of math, Bohr showed that
where n is the principal quantum number (i.e., n = 1, 2, 3, … and nothing else).

16. Line Spectra and the Bohr Model
We can show that
When ni > nf, energy is emitted.
When nf > ni, energy is absorbed

17. Line Spectra and the Bohr Model
Mathcad (Balmer Series)
CyberChem (Fireworks) video

18. Line Spectra and the Bohr Model: Balmer Series Calculations

20. Line Spectra and the Bohr Model: Balmer Series Calculations

21. Line Spectra and the Bohr Model
Limitations of the Bohr Model
Can only explain the line spectrum of hydrogen adequately.
Can only work for (at least) one electron atoms.
Cannot explain multi-lines with each color.
Electrons are not completely described as small particles.
Electrons can have both wave and particle properties.

22. The Wave Behavior of Matter
Knowing that light has a particle nature, it seems reasonable to ask if matter has a wave nature.
Using Einstein’s and Planck’s equations, de Broglie showed:
The momentum, mv, is a particle property, whereas  is a wave property.
de Broglie summarized the concepts of waves and particles, with noticeable effects if the objects are small.

23. The Wave Behavior of Matter
The Uncertainty Principle
Heisenberg’s Uncertainty Principle: on the mass scale of atomic particles, we cannot determine exactly the position, direction of motion, and speed simultaneously.
For electrons: we cannot determine their momentum and position simultaneously.
If Dx is the uncertainty in position and Dmv is the uncertainty in momentum, then

24. E = m c2 Energy and Matter Size of Matter Particle Property
Wave Property
Large – macroscopic
Mainly
Unobservable
Intermediate – electron
Some
Small – photon
Few
E = m c2

25. Quantum Mechanics and Atomic Orbitals
Schrödinger proposed an equation that contains both wave and particle terms.
Solving the equation leads to wave functions.
The wave function gives the shape of the electronic orbital. [“Shape” really refers to density of electronic charges.]
The square of the wave function, gives the probability of finding the electron ( electron density ).

26. Quantum Mechanics and Atomic Orbitals
Solving Schrodinger’s Equation gives rise to ‘Orbitals.’
These orbitals provide the electron density distributed about the nucleus.
Orbitals are described by quantum numbers.

27. Quantum Mechanics and Atomic Orbitals
Orbitals and Quantum Numbers
Schrödinger’s equation requires 3 quantum numbers:
Principal Quantum Number, n. This is the same as Bohr’s n. As n becomes larger, the atom becomes larger and the electron is further from the nucleus. ( n = 1 , 2 , 3 , 4 , …. )
Angular Momentum Quantum Number, . This quantum number depends on the value of n. The values of  begin at 0 and increase to (n - 1). We usually use letters for  (s, p, d and f for  = 0, 1, 2, and 3). Usually we refer to the s, p, d and f-orbitals.
Magnetic Quantum Number, m. This quantum number depends on  . The magnetic quantum number has integral values between -  and +  . Magnetic quantum numbers give the 3D orientation of each orbital.