1. From Indivisible to Quantum Mechanical Model of the Atom
Atomic Structure
From Indivisible to Quantum Mechanical Model of the Atom

2. Cartoon courtesy of NearingZero.net

3. Electrons and Quantum Theory
It turns out that the colored light is a mixture of quantized light energies.
A quantum of light is called a photon
There are several versions of light energy, and they all have 1 common characteristic…speed.
Light is a special type of non-ionizing radiation called electromagnetic radiation

4. The Behavior of Light
The EM spectrum is a broad range of wavelengths of energy which are all classified together because of their common speed.
Each of the different types of EMR all travel through space (vacuum) at a speed just under 300,000,000 m/s.
Radio, x-rays, ultraviolet,
infrared, microwaves, etc. are
versions of EMR

6. Light as a Wave Define one EMR from another
All waves, can be described in terms of 4 characteristics
Frequency
Wavelength
Amplitude
Speed
Define one EMR from another
Distinguishes one type of wave from another (sound, water, EMR, etc.)

7. Waves Waves transfer energy from one place to another
Think about the damage done by waves during strong hurricanes.
Think about placing a tennis ball in your bath tub, if you create waves at one it, that energy is transferred to the ball at the other = bobbing
Electromagnetic waves
have the same
characteristics as other
waves

8. Amplitude

9. Light as a Wave Wavelength (l):
the distance between successive crests of the wave.
the distance that the wave travels as it completes one full cycle of up and down motion

10. Light as a Wave Frequency (): How fast the wave oscillates.
Measured by the # of times a light wave completes a cycle of up and down motion per sec.
When a radio station
identifies itself it’s the
frequency used
Unit is a Hertz (sec-1)

11. Light as a Wave amplitude Amplitude:
Is the height of the wave measured from the origin to its crest, or peak
The brightness, or intensity of light depends on the amplitude of the light wave.
amplitude

12. Light as a Wave Speed (c):
Regardless of its wavelength, each type of EMR moves through space at a constant speed
3.00x108 m/s
Nothing can go faster than light,
it’s the fastest thing ever
(in a vacuum)
Light can be slowed down as it
passes through air, water, glass, etc.

13. Light as a Wave speed (frequency) = (wavelength) c  = 
Since light moves at a constant speed there is a mathematical relationship between frequency () & wavelength ()
The shorter the wavelength the higher the frequency
The longer the wavelength the lower the frequency
speed
(frequency) =
(wavelength) c  = 

14. Light as a Wave: White Light
As scientists strived to learn more about light, they discovered that white light (sunlight) is a mixture of 7 colors
Remember, white light encompasses only the visible portion of the spectrum
It is a mixture which can be separated by a prism into a continuous spectrum

15. Light as a Wave: White Light
The colors that combine to form white light are red, orange, yellow, green, blue, indigo, and violet (ROYGBIV)
The different colors have different wavelengths and frequencies
Long
Wavelength =
Low Frequency
Low ENERGY
Short
Wavelength =
High Frequency
High ENERGY

16. Scientists soon discovered that elements can also produce light.
Elements as Light
Scientists soon discovered that elements can also produce light.
If you energize gaseous elements they glow with a characteristic colored light
Neon glows orange, strontium glows red, copper glows green, etc.

17. Light as a Wave
If you take elemental light and pass it through a prism the light does not produce a continuous spectrum
Instead the spectrum splits into a characteristic pattern of lines of color.
It’s not a mixture of all wavelengths, but a mixture of specific, individual wavelengths
For instance with Hydrogen, you see 4 distinct lines of color

19. Quantum Theory
Before Max Planck came up with the model of quantized energy, scientists had no idea why excited elements glowed with light that was a mixture of specific wavelengths and not broad spectrums of wavelengths
If energy is lost or gained in discrete bundles with specific energy this would explain why we see individual lines of specific colors no matter how complex the spectra

20. Quantum Theory
Planck suggested that energy, instead of being given off in continuous waves, is instead given off in little packets of energy, or quanta.
The word quantum means a fixed amount, think of it as flashes of energy
Also called a photon when describing a quantum of light

21. Quantum Theory
Planck’s idea was that one quantum of energy (light) was related to its frequency by the equation: E = h 
The constant h (planck’s constant) has a value of x J-s, E is the energy, and  is the frequency of the radiation.
The energy in wave form that is abs-orbed or emitted by atoms, is restrict-ed to specific quantities (quantized)

22. Planck
Planck’s hypothesis: An object can only gain or lose energy by absorbing or emitting radiant energy in QUANTA.
Energy of radiation is proportional to frequency.
Note: Long wavelength
 small frequency
Short wavelength
 high frequency
increasing
wavelength
frequency
E = h • n

23. Photoelectric Effect An observed phenomenon, early 1900s
When light was shone on a metal, electrons were emitted from that metal
Light was known to be a form of energy, capable of knocking loose an electron from a metal
Therefore, light of any frequency could supply enough energy to eject an electron.

24. Photoelectric Effect
Light strikes the surface of a metal (cathode), and e- are ejected.
These ejected e- move from the cathode to the anode, and current flows in the cell.
A minimum frequency of light is used. If the frequency is above the minimum and the intensity of the light is increased, more e- are ejected.

25. Einstein Expands Planck’s Theory
Theorized that electromagnetic radiation had a dual wave-particle nature!
Behaves like waves and particles
Think of light as particles that each carry one quantum of energy = photons
Photons: a particle of electromagnetic radiation having zero mass and carrying a quantum of energy
Ephoton = h

26. Back to Photoelectric Effect
Einstein concluded:
Electromagnetic radiation is absorbed by matter only in whole numbers of photons
In order for an e- to be ejected, the e- must be struck by a single photon with minimum frequency

27. the range of energies that can break bonds.
Energy of Radiation
PROBLEM: Calculate the energy of 1.00 mol of photons of red light. l = 700 nm n = 4.29 x 1014 sec-1
E = h•n
= (6.63 x J•s)(4.29 x 1014 sec-1)
= x J per photon
E per mol = (2.85 x J/ph)(6.02 x 1023 ph/mol)
= kJ/mol
the range of energies that can break bonds.

28. Atomic Line Spectra
Bohr’s greatest contribution to science was in building a simple model of the atom.
It was based on understanding the SHARP LINE SPECTRA of excited atoms.
Niels Bohr ( )
(Nobel Prize, 1922)

29. Line Spectra of Excited Atoms
Excited atoms emit light of only certain wavelengths
The wavelengths of emitted light depend on the element. H Hg Ne

30. Atomic Spectra & Bohr Model
One view of atomic structure in early 20th century was that an electron (e-) traveled about the nucleus in an orbit.
1. Classically any orbit should be
possible and so is any energy.
2. But a charged particle moving in an electric field should emit energy.
End result should be destruction!

31. Bohr’s Model of Hydrogen Atom
Hydrogen did not produce a continuous spectrum
New model was needed:
Electrons can circle the nucleus only in allowed paths or orbits
When an e- is in one of these orbits, the atom has a fixed, definite energy
e- and hydrogen atom are in its lowest energy state when it is in the orbit closest to the nucleus

32. Bohr Model Continued…
Orbits are separated by empty space, where e- cannot exist
Energy of e- increases as it moves to orbits farther and farther from the nucleus
(Similar to a person climbing a ladder)

33. Bohr Model and Hydrogen Spectrum
While in orbit, e- can neither gain or lose energy
But, e- can gain energy equal to the difference between higher and lower orbitals, and therefore move to the higher orbital (Absorption)
When e- falls from higher
state to lower state, energy is
emitted (Emission)

34. Energy of state = - C/n2 where
So…
Bohr said classical view is wrong.
Need a new theory — now called QUANTUM or WAVE MECHANICS.
e- can only exist in certain discrete orbits
— called stationary states.
e- is restricted to QUANTIZED energy states.
Energy of state = - C/n2 where
C is a CONSTANT
n = QUANTUM NUMBER, n = 1, 2, 3, 4, ....

35. Bohr Cont…
If e-’s are in quantized energy states, then DE of states can have only certain values. This explains sharp line spectra.
H atom
07m07an1.mov
n = 1
n = 2
E = -C (1/22)
E = -C (1/12)
4-H_SPECTRA.MOV

36. This is exactly in agreement with experiment!. n = 1 2
Energy
Putting Numbers to it
Calculate DE for e- in H “falling” from n = 2 to n = 1 (higher to lower energy) .
DE = Efinal - Einitial = -C[(1/12) - (1/2)2] = -(3/4)C
(-ve sign for DE indicates emission (+ve for absorption)
since energy (wavelength, frequency) of light can only be +ve it is best to consider such calculations as DE = Eupper - Elower
C has been found from experiment. It is now called R,
the Rydberg constant. R = 1312 kJ/mol or 3.29 x 1015 Hz
so, E of emitted light = (3/4)R = x 1015 Hz
and l = c/n = nm (in ULTRAVIOLET region)
This is exactly in agreement with experiment!

37. n High E Short l High n Low E Long l Low n Hydrogen atom spectra
Visible lines in H atom
spectrum are called the
BALMER series. 6 5 3 2 1 4 n
Energy
Ultra Violet
Lyman
Visible
Balmer
Infrared
Paschen
En = -1312 n2

38. Quantum Mechanics
Uses mathematical equations to describe the wave properties of subatomic particles
It’s impossible to know the exact position, speed and direction of an electron (Heisenberg Uncertainty Principle)
So Bohr’s “orbits” were replaced by orbitals
A wave function that predicts an electron’s energy and location within an atom
A probability cloud in which an electron is most likely to be found

39. Orbits
Orbitals
- Bohr
- 2-dimensional ring
- Electron is a fixed distance from nucleus
- 2, 8, or 18 electrons per orbit
- Quantum Mechanics
- 3-dimensional space
- Electrons are a variable distance from nucleus
- 2 electrons per orbital

40. Wave Particle Duality
Experimentally, DeBroglie found that light had both wave and particle properties
Therefore DeBroglie assumed that any particle (including electrons) traveled in waves
Wavelengths must be quantized or they would cancel out

41. Heisenberg’s Uncertainty Principle
Due to the wave and particle nature of matter, it is impossible to precisely predict the position and momentum of an electron
SchrÖdinger’s equation can be used to determine a region of probability for finding an electron (orbital)
Substitute in a series of quantum numbers to solve the wave function

42. Definitions Probability  likelihood
Orbital  wave function; region in space where the probability of finding an electron is high
SchrÖdinger’s Wave Equation states that orbitals have quantized energies
But there are other characteristics to describe orbitals besides energy

43. Wave-Particle Duality
de Broglie’s experiments suggested that e- has wave-like properties.
Thomson’s experiments suggested that e- has particle-like properties
measured charge-to-mass ratio
And so we begin looking at the configuration of electrons…