Download The Spin Quantum Number

spin quantum number
The Spin Quantum Number
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spin quantum number
Summary of Bohr’s Model (1913)
Electrons are in different orbits at fixed distances from nucleus.
Electrons that leave one orbit must move to another orbit.
Electrons only change orbits if specific amounts (quanta) of
extra energy from the outside world are involved.
Electrons that receive enough extra energy from the outside
world can leave the atom they are in.
Electrons that return to orbits they used to reside in give up
the extra energy they acquired when they moved in the first
place.
Electronic energy given up when electrons move back into an
original orbit often shows up as a specific color light.
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spin quantum number
Three Quantum Number Bohr Atom Model
Two quick review questions.
(1) What are the 5 lowest energy
terms (orbits) for a nitrogen?
2
2
1
1
1
1s , 2s , 2p , 2p , 2p
x
y
z
2s
2p y
1s
2p x
2p z
(2) What are the names of the lowest energy terms
(orbits) for a carbon atom. (Remember that carbon’s
atomic number is 6)
2
2
1s , 2s , 2p
1
1
2p
x ,
y
The carbon atom has 6 protons and 6 electrons.
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spin quantum number
Four Quantum Number Bohr Atom Model
The three quantum number atom model was
very successful explaining various light
energies observed in the spectra of atoms.
2s
2p y
1s
2p x
2p z
However, in some cases, there were still spectra lines
that were clearly different colors but very close together.
A fourth and final quantum number was added to
the Bohr model to account for these light waves that
differed by only a small amount of energy.
The spin quantum number
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spin quantum number
Four Quantum Number Bohr Atom Model
n the principal quantum number
l the angular momentum
2s
2p y
(azimuthal) quantum number
m the magnetic quantum number
s the electron spin quantum number
Since each electron has a negative charge, two
electrons do not like to be near each other.
Originally, it was imagined that an electron spins on its
axis just as the earth spins on its axis.
If two electrons had to be close to each other, one
would spin one way (clockwise) and the other would
spin the other way (counter clockwise.)
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1s
2p x
2p z
spin quantum number
Four Quantum Number Bohr Atom Model
n
the principal quantum number
l
the angular momentum
(azimuthal) quantum number
m
the magnetic quantum number
s
the electron spin quantum number
2s
2p y
1s
2p x
2p z
Each spin direction, clockwise and counter clockwise, was
assigned a value and identified as the s quantum number value.
The spin quantum number
value for an electron
spinning clockwise
is equal to + 0.5.
Most of the time, people say 1/2 instead of 0.5.
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spin quantum number
Four Quantum Number Bohr Atom Model
n
the principal quantum number
l
the angular momentum
(azimuthal) quantum number
m
the magnetic quantum number
s
the electron spin quantum number
EXAMPLE: Using the four quantum number
model, uniquely identify the lowest energy
term (orbit) for a hydrogen atom.
The spin quantum number
value for an electron
spinning clockwise
2s
2p y
1s
2p x
2p z
1, 0, 0, +1/2
is equal to + 0.5.
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spin quantum number
Four Quantum Number Bohr Atom Model
n
the principal quantum number
l
the angular momentum
(azimuthal) quantum number
m
the magnetic quantum number
s
the electron spin quantum number
2s
2p y
1s
2p x
2p z
The spin quantum number
value for an electron
spinning clockwise
is equal to + 1/2.
The spin quantum number
value for an electron
spinning counter clockwise
is equal to - 1/2.
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spin quantum number
Four Quantum Number Bohr Atom Model
n
the principal quantum number
l
the angular momentum
(azimuthal) quantum number
m
the magnetic quantum number
s
the electron spin quantum number
If two electrons have to reside close together,
they will spin in opposite directions.
s = +1/2
s = +1/2
-1/2 = s
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spin quantum number
Four Quantum Number Bohr Atom Model
n
the principal quantum number
l
the angular momentum
(azimuthal) quantum number
m
the magnetic quantum number
s
the electron spin quantum number
Using the four quantum number model,
describe the lowest energy term (orbit)
for a hydrogen atom.
Using the four quantum number model,
describe the two lowest energy term
(orbits) for a helium atom.
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1, 0, 0, +1/2
1, 0, 0, +1/2
1, 0, 0, -1/2
spin quantum number
Four Quantum Number Bohr Atom Model
Try two more examples.
(1) Name the three lowest energy
terms (orbits) for a lithium atom.
Remember that lithium is atomic number 3.
1, 0, 0, +1/2
1, 0, 0, -1/2
2, 0, 0, +1/2
1, 0, 0, +1/2
(2) Name the four lowest energy terms 1, 0, 0, -1/2
(orbits) for a beryllium atom
2, 0, 0, +1/2
Remember that beryllium is atomic number 4.
2, 0, 0, -1/2
EVERY electron has its own individual
set of 4 quantum number values
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spin quantum number
Four Quantum Number Bohr Atom Model
The Exclusion Principle
No two electrons in the same atom
can have the same set of 4 quantum
number values.
Wolfgang Ernst Pauli
Wolfgang Ernst Pauli
1900 -1958
Nobel prize in 1945
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spin quantum number
Four Quantum Number Bohr Atom Model
n
the principal quantum number
l
the angular momentum
(azimuthal) quantum number
m
the magnetic quantum number
s
the electron spin quantum number
EVERY electron has its own individual set of quantum number values.
Short hand way to use 4 quantum numbers
to describe electron energy levels.
The three lowest energy terms (orbits) for a lithium atom.
1, 0, 0, +1/2
1, 0, 0, -1/2
2, 0, 0, +1/2
The short hand notation for lithium atom energy levels.
1s
2s
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spin quantum number
Four Quantum Number Bohr Atom Model
The short hand notation for lowest
lithium atom energy levels
1s 2s
Try three more examples.
(1)
(2)
(3)
What are the lowest energy
terms (orbits) for a nitrogen
atom (atomic number 7)?
1s 2s 2p 2p 2p
x y z
What are the lowest energy
terms (orbits) for a fluorine
atom (atomic number 9).
1s 2s 2p 2p 2p
x y z
What are the lowest energy
terms (orbits) for a neon atom
(atomic number 10).
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1s 2s 2p 2p 2p
x y z
spin quantum number
Four Quantum Number Bohr Atom Model
Atoms from atomic number 1 (hydrogen)
through atomic number 18 (argon) fill their
energy levels (orbits) using a repetitive
pattern.
2 electrons
1s
2 electrons
2s
2 electrons
3s
6 electrons
[2p 2p 2p ]
x y z
6 electrons
[3p 3p 3p ]
x y z
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A maximum of 9
energy states
A maximum of
2 electrons in
each energy
state
spin quantum number
Four Quantum Number Bohr Atom Model
1
H
3
Li
11 Na
19
K
2 He
4 Be
12 Mg
5B
6C
7N
8O
9F
10 Ne
13 Al
14 Si
15 P
16 S
17 Cl
18 Ar
Various shorthand ways to describe the electron energy
levels for beryllium, fluorine and some of the other first
18 atoms in the periodic table are shown below.
1s
1s
1s 2s
1s 2s
Ne 3s
Ne 3s
Ar 4s
Ar 4s
Be 2p
Be 2p 2p 2p
x
Y
Z
x
2 2 6
1s 2s 2p
Are there other common shorthand notations for Fluorine?
1s
2s
2p x 2p y 2p z
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And/or
1s
2
2
5
, 2s , 2p
spin quantum number
Summary of Four Quantum
Number Bohr Atom Model
• Electrons within an atom can be completely identified as
unique electrons with the aid of 4 quantum numbers.
• These 4 quantum numbers are called
n the principal quantum number
the angular momentum
l
(azimuthal) quantum number
m the magnetic quantum number
s the electron spin quantum number
• No two electrons in the same atom can have the same value
for all four of these quantum numbers.
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spin quantum number
Summary of Four Quantum
Number Bohr Atom Model
• Electrons returning to their “ground” state can emit light
with a unique frequency (energy).
• Atoms are filled with electrons from the orbit closest to
the nucleus to the orbit furthest from the nucleus.
• The diagonal fill rule predicts the way electrons fill orbits.
• The Bohr model does not explain why the 4s orbit is closer to
the nucleus than the 3d orbit.
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spin quantum number
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