1. Chapter 7: The quantum-mechanical model of the atom

2. The nature of light
Light – electromagnetic radiation that is composed of oscillating electric and magnetic fields which are perpendicular to each other
Magnetic field – a region in space where a magnetic particle will experience a force
electric field – a region in space where an electrically charged particle will experience a force
Light travels at the speed of….. light!
3.00 x 108 m/s
The letter “c” can be used to stand for light
Wave-particle duality – light can behave as a particle and a wave

3. Light’s wave nature
A wave oscillates, giving an amplitude and a wavelength
amplitude – the vertical height of a crest in the wave
wavelength (λ)– the length of the wave
Visible light has a wavelength between nm
Frequency (v) – the number of cycles of a wave that pass through a stationary point in a given time period
Units of frequency = hertz = Hz = cycles/second = 1/s = s-1

4. The electromagnetic spectrum
Electromagnetic spectrum – gives ranges of types of electromagnetic radiation based on wavelength or frequency or energy
Radio – microwave – infrared – visible light – ultraviolet – X-ray – gamma ray

5. Practice
What is the wavelength of a beam of light that has a frequency of 4.62 x 1014 Hz
c = 3 x 108 m/s
v = 4.62 x 1014 Hz
What type of electromagnetic radiation is this?

6. Wave interference
Waves can interact with other waves through interference
Depending on the degree of interference, waves can produce constructive or destructive interference

7. Diffraction Diffraction – when a wave bends around an obstacle or slit
Slit must have comparable size to the wavelength
This is different than how a particle would behave

8. Diffraction patterns

9. Light’s particle nature
photo electric effect – when a metal emits electrons after light shines upon them
Light energy comes in discrete packets
Photon or quantum of light – a packet of light
Each photon has an associated energy dependent on its frequency (v)
h = Planck’s constant = 6.62 x (J*s)

10. Photoelectric effect continued
For a photon of light to be able to kick out an electron off of a metal, it must have at least a certain amount of energy, it must pass a certain threshold
φ = Binding energy of an emitted electron
All excess energy over the threshold turns into kinetic energy of the electron

11. Practice
A nitrogen gas laser pulse with a wavelength of 337 nm contains 3.83 mJ of energy. How many photons does the pulse contain?
Can a photon from this type of light excite an electron from Aluminum, which has a threshold energy of 6.88 x 10-19J?

12. Atomic spectroscopy
When an atom absorbs energy it can reemit that energy as light
Depending on the atom, different colors can be emitted
Although one color may be perceived, an emission spectrum is produced

13. Sodium Potassium Lithium Barium

14. Bohr Model
Niels Bohr ( ) proposed that electrons orbit the nucleus at different energy levels
An emission spectrum that is produced is derived from electron energy level transitions

15. Hydrogen electronic transitions
The energy of an electron in an energy level (n) is represented from the equation below
Higher n value = less negative energy = higher energy
En is negative because the electrons energy is lowered by its interaction with the positively charged nucleus
As n increases, the rate at which the energy increases is less
The difference in energy between the n =2 and n = 3 is less than the difference between n = 1 and n = 2

17. If an electron jumps from one energy level to another, the change in energy can be calculated
nf = final energy level
ni = initial energy level

18. Determine the wavelength of light emitted when an electron in a hydrogen atom makes a transition from an n = 6 to n = 5 energy level.

19. The wave properties of matter
Electrons can also display wave properties
Can also produce diffraction patterns from two closely spaced slits

20. The de Broglie wavelength
Since we can describe electrons as having wave properties, we can utilize wave equations to describe electrons
h = planck’s constant (kg*m2)/(s2)
m = mass of electron x kg
v = velocity of electron in m/s
If you know the velocity of an electron, you its wavelength

21. Schrödinger’s cat
An electron can exhibit wave and particles properties (wave-particle duality)
It can exist in two states at the same time, but upon observation, one state is observed
Erwin Schrödinger ( ) proposed a thought experiment where a sealed box contains a cat, a radioactive atom, and a device that will kill the cat if the radioactive atom emits a particle upon radioactive decay
The radioactive atom exists in both the emitted and non emitted states, making the cat both dead and alive

22. The uncertainty principle
Although electrons can exist as waves and particles, observation forces it into one state, excluding the other state
Complementary properties – properties that exclude each other, the more we know one the less we know the other
Position and velocity of an electron are also complementary properties
Werner Heisenberg’s ( ) formulized Heisenberg’s uncertainty principle
Δx = uncertainty in position
Δv = uncertainty in velocity

23. Indeterminacy
For macroscale objects Newton’s laws of motion are useful and position and velocity can both be known simultaneously, and also considered deterministic
Deterministic – the present determines the future
For electrons the position and velocity are not known, so its future is uncertain
Indeterminacy – the future path can not be precisely determined
A probability map is more effective at determining the future of the electron

24. Atomic orbitals
Orbital – a probability distribution map of where an electron is likely to be found
A house for the electrons
Though position is uncertain, the energy of the orbital is
Quantum numbers specify properties of a orbital and an electron that may reside inside of it
n, l, ml, ms

25. Principal quantum number (n)
n – determine the size and energy of an orbital
The value of n is an integer
n = 1,2,3,... and so on
En = energy for an electron in a hydrogen orbital

26. Angular momentum quantum number (l)
l – determines the shape of an orbital
The value of l can range be 0,1,2,3,… (n – 1)
The value of n determine the possible l values
If n = 2, l can be 0 or 1
l can also be represented with letters to avoid confusion

27. Magnetic quantum number (ml)
ml - an integer that specifies the orientation of the orbital
Possible values determined by the l value
-l to +l
l = 2, then ml can be -2, -1, 0, +1, +2

28. Spin quantum number (ms)
Electrons are considered to have a spin
Due to a electrical particle spinning it also creates a magnetic field
ms – refers to the orientation of the spin of the electron in an orbital
ms = +1/2 = spin up
ms = -1/2 = spin down

29. The shapes of atomic orbitals
The angular momentum quantum number (l) defines the type/shape of an orbital
A probability density represents an orbital, being the region where an electron can exist in an atom
A radial distribution function shows the probability of finding an electron within a thin spherical shell at a distance r from the nucleus
Probability density for an 1s orbital

30. s orbitals (l = 0)
When l = 0, you have an s orbital which is has a spherical shape
Depending on the principle quantum number you will have a smaller or larger s orbital
n = 1 , l = 0  1s orbital
n = 2 , l = 0  2s orbital
n = 3 , l = 0  3s orbital
Since l = 0, and the formula for ml = -l to +l, ml = 0
There is only one s orbital per principle level

31. p orbitals (l = 1)
When l = 1, you have an p orbital which is has a dumbbell shape
n = 1 , l = 1  1p orbital DOESN’T EXIST
n = 2 , l = 1  2p orbital
Since l = 1, and the formula for ml = -l to +l, ml = -1, 0, +1
There are three p orbitals per principle level
ml = -1  px ml = 0 py ml = +1 pz

32. d orbitals (l = 2)
When n = 3 or greater and l = 2, you have an d orbitals
Since l = 2, ml = -2,-1, 0, +1, +2
There are five d orbitals per principle level

33. f orbitals (l = 3)
When n = 4 or greater and l = 3, you have an f orbitals
Since l = 3, ml = -3, -2,-1, 0, +1, +2, +3
There are seven f orbitals per principle level

34. Practice
If n = 4, which of the following values for l are not allowed?
1, 3, 4, 7
If l = 3, what is the correct ml values allowed?
A. -1, 0, +1
B. 0, 1, 2, 3
C. -2, -1, 0, +1, +2
D. -3, -2, -1, 0, +1, +2, +3
Which type of orbital is represented by the previous l value?

35. The overall shape of an atom
Most atoms have many electrons that fill up many orbitals
The overall shape of the atom is a collection of all those orbitals s, p, d, f, n= 1,2,3,4,…
The overall shape is like a sphere

36. Schrödinger’s Chapter 7 (finished/not finished)