TEMA PARA LA MATERIA DE QUÍMICA...t/t

1. Unit IV: Quantum Mechanics and
Bonding
QBA Miguel A. Castro Ramírez

2. Light
• Before 1900, scientists thought that light
behaved only as wave
• discovered that also has particle-like
characteristics

3. Light as a Wave
• electromagnetic radiation:
– form of energy that acts as a wave as it travels
– includes: visible light, X rays, ultraviolet and
infrared light, microwaves, and radio waves
• All forms are combined to form
electromagnetic spectrum

4. Light as a Wave

5. Light as a Wave
• all form of EM radiation travel at a speed of 3.0
x 108 m/s in a vacuum
• it has a repetitive motion
• wavelength: (λ) distance between points on
adjacent waves; in nm (109nm = 1m)
• frequency: (ν) number of waves that passes a
point in a second, in waves/second
Inversely proportional!
c = λυ

7. Photoelectric Effect
• when light is shone on a piece of metal,
electrons can be emitted
• no electrons were emitted if the light’s
frequency was below a certain value
• scientists could not explain this with their
classical theories of light
• Ex: coin-operated sift drink machine

8. Photoelectric Effect
• Max Planck: a German physicist
• suggested that an object emits energy in the
form of small packets of energy called quanta
• quantum- the minimum amount of energy that
can be gained or lost by an atom
E = hν
Planck’s constant (h): 6.626 x 10-34 J*s

9. Photoelectric Effect
• Einstein added on to Planck’s theory in 1905
• suggested that light can be viewed as stream
of particles
• photon- particle of EM radiation having no
mass and carrying one quantum of energy
• energy of photon depends on frequency

10. Photoelectric Effect
• EM radiation can only be absorbed by matter
in whole numbers of photons
• when metal is hit by light, an electron must
absorb a certain minimum amount of energy
to knock the electron loose
• this minimum energy is created by a minimum
frequency
• since electrons in different metal atoms are
bound more or less tightly, then they require
more or less energy

11. H Line-Emission Spectrum
• ground state- lowest energy state of an atom
• excited state- when an atom has higher
potential energy than it has at ground state
• line-emission spectrum- series of wavelengths
of light created when visible portion of light
from excited
atoms is shined through a prism

12. H Line-Emission Spectrum
• scientists using classical theory expected atoms
to be excited by whatever energy they absorbed
• continuous spectrum- emission of continuous
range of frequencies of EM
radiation

13. H Line-Emission Spectrum
• Why had hydrogen atoms only given off specific
frequencies of light?
current Quantum Theory attempts to explain this
using a new theory of atom

14. H Line-Emission Spectrum
• when an excited atom falls back to ground
state, it emits photon of radiation
• the photon is equal to the difference in energy
of the original and final states of atom
• since only certain frequencies are emitted, the
differences between the states must be
constant

15. Bohr Model
• created by Niels Bohr
(Danish physicist)
in 1913
• linked atom’s electron with emission
spectrum
• electron can circle nucleus in certain paths, in
which it has a certain amount of energy

16. Bohr Model
• Can gain energy by moving
to a higher rung on ladder
• Can lose energy by moving
to lower rung on ladder
• Cannot gain or lose while on
same rung of ladder

17. Bohr Model
a photon is released
that has an energy
equal to the
difference between
the initial and final
energy orbits

18. Bohr Model
• problems:
– did not work for other atoms
– did not explain chemical behavior of atoms

19. Introduction to Quantum Theory
• Quantum Theory-
describes mathematically the wave properties
of electrons

20. Electrons as Waves
• In 1924, Louis de Broglie
(French scientist)
• suggested the way quantized
electrons orbit the nucleus is similar to behavior
of wave
• electrons can be seen as waves confined to the
space around a nucleus
• waves could only be certain frequencies since
electrons can only have certain amounts of
energy

21. Electrons as Waves
c
c = λv v=
λ hc
E=
λ
E = hv
h hc
λ= = mc 2
mv λ E = mc 2
shows that anything with both mass and velocity
has a corresponding wavelength

22. Uncertainty Principle
• In 1927 by Werner Heisenberg (German
theoretical physicist)
• electrons can only be detected by their
interaction with photons
• any attempt to locate a specific electron with
a photon knocks the electron off course
• Heisenberg Uncertainty Principle- it is
impossible to know both the position and
velocity of an electron

23. Schrödinger Wave Equation
• In 1926, Erwin Schrödinger
(Austrian physicist)
• his equation proved that
electron energies are quantized
• only waves of specific energies provided
solutions to his equation
• solutions to his equation are called wave
functions

24. Schrödinger Wave Equation
• wave functions give only the probability of
finding an electron in a certain location
• orbital- 3D area around a nucleus that has a
high probability of containing an electron
• orbitals have different shapes and sizes

25. Quantum Numbers
• specify the properties of atomic orbitals and
of electrons in orbitals
• the first three numbers come from the
Schrödinger equation and describe:
– main energy level
– shape
– orientation
• 4th describes state of electron

26. 1 Quantum Number
st
Principal Quantum Number: n
• main energy level occupied by electron
• values are all positive integers (1,2,3,…)
• As n increases, the electron’s energy and its
average distance from the nucleus increase
• multiple electrons are in each level so have
the same n value
• the total number of orbitals in a level is equal
to n2

27. 1 Quantum Number
st
Energy

28. 2 Quantum Number
nd
Angular Momentum Quantum Number: l
• indicates the shape of the orbital (sublevel)
• the possible values of l are 0 to n-1
• each atomic orbital is designated by the principal
quantum number followed by the letter of the
sublevel

29. 2 Quantum Number
nd
s orbitals:
• spherical
• l value of 0
• Max 2 electronsd

30. 2 Quantum Number
nd
p orbitals:
• dumbbell-shaped
• l value of 1
• Max. 6 electrons

31. 2 Quantum Number
nd
d orbitals:
• various shapes
• l value of 2
• Max. 10 electrons

32. 2 Quantum Number
nd
f orbitals:
• various shapes
• l value of 3
• Max. 14 electrons

33. 2 Quantum Number
nd
Level Sublevels Sublevels
0 1 2 3
0 1 2
0 1
0

34. 3 Quantum Number
rd
Magnetic Quantum Number: ml
• indicates the orientation of an orbital around
the nucleus
• has values from -l +l
• specifies the exact orbital that the electron is
contained in
• each orbital holds maximum of 2 electrons

35. Energy Sublevels # Orbitals Total # of
Level in Level in Orbitals in
(n) Sublevel Level
1 l=0, s 1 1
2 l=0, s 1 4
l=1, p 3
3 l=0, s 1 9
l=1, p 3
l=2, d 5
4 l=0, s 1 16
l=1, p 3
l=2, d 5
l=3, f 7

36. 4 Quantum Number
th
Spin Quantum Number: ms
• indicates the spin state of the electron
• only 2 possible directions
• only 2 possible values: -½ and +½
• paired electrons must
have opposite spins

37. Energy Level 1
n l ml ms
1 0 0 -½,+½

38. Energy Level 2
n l ml ms
2 0 0 -½,+½
1 -1 -½,+½
0 -½,+½
+1 -½,+½

39. Energy Level 3
n l ml ms
3 0 0 -½,+½
1 -1 -½,+½
0 -½,+½
+1 -½,+½
2 -2 -½,+½
-1 -½,+½
0 -½,+½
+1 -½,+½
+2 -½,+½

40. Energy Level 4
n l ml ms l ml ms
4 0 0 -½,+½ 3 -3 -½,+½
1 -1 -½,+½
-2 -½,+½
0 -½,+½
+1 -½,+½ -1 -½,+½
2 -2 -½,+½ 0 -½,+½
-1 -½,+½ +1 -½,+½
0 -½,+½
+2 -½,+½
+1 -½,+½
+2 -½,+½ +3 -½,+½

41. Homework
1. Give the values of n, ℓ, mℓ and ms for every orbital
with n = 6.
2. Indicate whether the set of quantum numbers (n, ℓ,
mℓ) exits or not.
a. 1, 1, 0 e. 8, 1, 0
b. 5, 4, –3 f. –2, 1, +1
c. 3, 2, –3 g. 4, 2, –1
d. 6, 7, +7 h. 7, 3, +4
3. Draw the shapes (including the orientation) of all
the s, p and d orbitals.

42. Homework
4. Which orbital in each of the following pairs is higher in
energy?
a. 5s or 5d
b. 4s or 3p
c. 6s or 4d
5. What is the maximum number of electrons in an atom that
can have these quantum numbers?
a) n = 2
b) n = 3,
c) n = 3, l = 1
d) n = 4, l = 2
e) n = 5, l= 3, ml=3