5. RUTHERFORD’S MODEL
• The atom contains a tiny dense center called the
nucleus.
• The nucleus is essentially the entire mass of the
atom.
• The nucleus is positively charged.
• The electrons move around in the empty space
of the atom surrounding the nucleus.
7. PROBLEMS WITH
RUTHERFORD’S NUCLEAR MODEL
• Electrons are moving charged particles.
• According to classical physics, moving charged
particles give off energy. Therefore, electrons
should constantly be giving off energy.
• The electrons should lose energy, crash into the
nucleus, and the atom should collapse!
8. BOHR’S MODEL
• The electrons travel in orbits of
specific energies that are at a
fixed distance from the nucleus.
• Electrons emit radiation when
they “jump” from an orbit with
higher energy down to an orbit
with lower energy.
• Ground State Excited State
10. QUESTION:
WHY DOES THE (BOHR) ATOM RESTRICTS ITS
ELECTRONS TO ORBIT THE NUCLEUS AT A
CERTAIN FIXED DISTANCE?
11. THE DUAL NATURE
OF THE ELECTRON
• Louis de Broglie proposed that subparticles
(electron) could have wavelike properties.
• An electron bound to the nucleus behaves like a
standing wave.
• Louis de Broglie argued that if an electron does
behave like a standing wave, the length of the
wave must fit the circumference of the orbit
exactly.
12. THE DUAL NATURE
OF THE ELECTRON
• It was predicted that the wavelength of a particle
was inversely proportional to its momentum.
14. THE UNCERTAINTY PRINCIPLE
• HEISENBERG UNCERTAINTY PRINCIPLE:
- It is impossible to simultaneously both the
momentum (p) and the position of a particle with
certainty.
• “The more accurately you know the position of
the electron, the less you know about its speed,
and vice versa.”
15. THE UNCERTAINTY PRINCIPLE
DETERMINACY VS INDETERMINACY
• According to classical physics, particles move in a path
path determined by the particle’s velocity, position,
and forces acting on it.
• Because we cannot know both the position and
velocity of an electron, we cannot predict the path it
will follow.
• The best we can do is to describe the probability and
electron will be found in a particular region.
16. SCHRÖDINGER’S EQUATION
• Schrödinger’s equation allows us to calculate the
probability of finding an electron with a
particular amount of energy at a particular
location in the atom.
• The Schrödinger equation specifies the possible
energy states the electron can occupy in a
hydrogen atom and identifies the corresponding
wave functions.
17. THE QUANTUM NUMBERS
• In quantum mechanics, three quantum numbers are
required to describe the distribution of electrons.
- principal quantum number (n)
- angular momentum number (l)
- magnetic momentum number (ml)
• These quantum numbers are used to describe the
atomic orbitals and to label electrons that resides in
them.
18. THE QUANTUM NUMBERS
•The Principal Quantum Number (n)
- have integral values 1, 2, 3, and so forth
- the value of n determines the energy of
an orbital
- the n also relates to the distance of the
electron from the nucleus
- principal energy level “shell”
19. THE QUANTUM NUMBERS
•The Angular Momentum Quantum Number (l)
- tells us the “shape” of the orbitals
- depends on the value of the principal
quantum number n
- for the given value of n, the l has possible
integral values of 0 – (n-1)
(l) 0 1 2 3 4 5
Orbital Name s p d f g h
20. THE QUANTUM NUMBERS
•The Angular Momentum Quantum Number (l)
- sublevel“subshells”
- s (sharp) – spherical
- p (principal) – dumbbell
(2 balloons tied at the knots)
- d (diffuse) – clover
(4 balloons tied at the knots)
- f (fundamental) – to complex to describe
(8 balloons tied at the knots)
21. THE QUANTUM NUMBERS
• The Magnetic Quantum Number (ml)
- describes the orientation of the orbital in
space
- values are integers from −l to +l
- “orbitals”
22. THE QUANTUM NUMBERS
•The s sublevel
- all s orbitals are
spherical, and their sizes
increases with increasing
n.
23. THE QUANTUM NUMBERS
•The p sublevel
- all p orbitals are
dumbbell-shaped and
are oriented along three
perpendicular axes (x, y,
and z).
24. THE QUANTUM NUMBERS
•The d sublevel
- 4 d orbitals are
clover-shaped lying in
different planes. 1 d
orbital has its own
unique shape.
29. THE QUANTUM NUMBERS
• The Electron Spin Quantum Number (ms)
- has a value of +1/2 or -1/2
- electron spin-up if ms is +1/2, spin-down if
ms is -1/2
30. THE QUANTUM NUMBERS
• Write the four quantum numbers (n, l, ml, and
ms) for an electron in a 3p orbital.
Answer:
(3,1,-1,+1/2) (3,1,-1,-1/2)
(3,1,0,+1/2) (3,1,0,-1/2)
(3,1,+1,+1/2) (3,1,+1,+1/2)
31. THE QUANTUM NUMBERS
•Explanation: 3p orbital
We know that the n is 3 and the l is 1 since we
are dealing with p orbital. Since l is 1, our ml are -
1,0, and +1. And because ms can be either +1/2 or
-1/2, we conclude that there are six possible ways
to designate the electrons in 3p orbital.
32. LET’S DO THIS!
On a 1 whole sheet of paper, designate the
electrons using the four quantum numbers in the
given orbitals:
1. 1s
2. 2p
3. 3d
4. 4f
5. 5s
33. THE PAULI
EXCLUSION PRINCIPLE
• The Pauli Exclusion Principle states that “no two
electrons in an atom can have the same set of four
quantum numbers.
Which of the following orbital diagrams correctly
follows the Pauli Exclusion Principle?
34. DIAMAGNETISM
AND PARAMAGNETISM
•Diamagnetic substances do not contain net
unpaired spins and are slightly repelled by a
magnet.
• Paramagnetic substances contain net unpaired
spins and are attracted by a magnet.
IS LITHIUM (Li) DIAMAGNETIC OR
PARAMAGNETIC?
35. HUND’S RULE
• Hund’s Rule states that the most stable arrangement
of electrons in subshells is the one with the greatest
number of parallel spins.
Which of the following orbital diagrams of Carbon in its
2p orbitals satisfy the Hund’s Rule?
36. AUFBAU PRINCIPLE
•The Aufbau principle dictates that as protons are
added one by one to the nucleus to build up the
elements, electrons are similarly added to the
atomic orbitals.
37. LET’S TRY!
• Draw the orbital diagrams in each energy level
and write the quantum numbers of the electrons
that can be found on the highest energy level
while satisfying the Pauli’s Exclusion Principle and
the Hund’s Rule:
1. Carbon – 1s2 2s2 2p2
2. Neon – 1s2 2s2 2p6
3. Sulfur – 1s2 2s2 2p6 3s2 3p4
