quantum mechanics
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QUANTUM MECHANICS
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NEILS BOHR
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HELIUM ATOM
+N
N
+-
-
proton
electron
neutron
Shell
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3 p+
4 n02e– 1e–
Li shorthand
Bohr - Rutherford diagrams
2 p+
2 n0
He
3 p+
4 n0
Li
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11 p+12 n°
2e– 8e– 1e–
Na
8 p+8 n°
2e– 6e–
O
4 p+5 n°
Be
5 p+6 n°
B
13 p+14 n°
Al
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LOUIS de BROGLIE - 1924
• He proposed that electron behaves like a wave, specifically a standing wave. A standing wave is a wave that does not travel down its medium.
• A standing wave is obtained when one point (called the node) in the middle of the wave is stationary.
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WERNER HEISENBERG - 1927
• UNCERTAINTY PRINCIPLE• States that there is NO way to determine
both the precise location and momentum (mass X velocity) of small particles at the same time.
• Principle implies that if we could measure the momentum of an electron accurately, we could NOT determine its location at the same time.
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QUANTUM•values used to
express the “quanta” or
the packets of energy
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SCHRODINGER – 1926
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QUANTUM MECHANICS
•“wave mechanics” is a
field that described the
behavior, as well as the energies,
of particles.
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QUANTUM NUMBERS
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QUANTUM NUMBERS
• principal quantum number
• orbital quantum number
• magnetic quantum number
• electron spin quantum number
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PRINCIPAL QUANTUM NUMBER (n)
• Corresponds to the
energy level numbers. As (n) increases, the average distance of an electron from the nucleus also increases.
• The larger the (n) the larger the atomic orbital.
+N
N
+
n=1n=2n=3
n= so on…
K L M
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ORBITAL QUANTUM NUMBER (l)
• AZIMUTHAL
• The sublevels that describes the shape of the atomic orbitals.
• Examples: l = 0 s orbital
l = 1 p orbitall = 0 d orbital
l = 1 f orbital
+N
N
+
n=1n=2n=3
n= so on…
K L M
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POSSIBLE ANGULAR MOMENTUM QUANTUM
NUMBERS (l)PRINCIPAL
ENERGY LEVEL (n)
(n – 1) POSSIBLE (l)
VALUES: 0 TO (n – 1)
SUBLEVELS
1 1 – 1 = 0 0 s2 2 – 1 = 1 0,1 s,p3 3 – 1 = 2 0,1,2 s,p,d4 4 – 1 = 3 0,1,2,3 s,p,d,f5 5 – 1 = 4 0,1,2,3,4 s,p,d,f,g6 6 – 1 = 5 0,1,2,3,4,5 s,p,d,f,g,h
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MAGNETIC QUANTUM NUMBER (ml)
• Describes the orientation
of the atomic orbital in space. The magnetic quantum number can only have (2l X 1) integral values for a particular l.
• Example:
l = 1[ (2 X 1) + 3] or 3 ml
Values. These 3 ml values are -1, 0, and +1
+N
N
+
n=1n=2n=3
n= so on…
K L M
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NUMBER OF ATOMIC ORBITALS PER SUBLEVEL
n l SUBLEVEL 2l + 1 ml VALUES Number of Atomic Orbital
1 0 1s 2(0) + = 1 0 12 0 2s 2(0) + = 1 0 13 1 2p 2(1) + = 3 1, 0, -1 3
0 3s 2(0) + = 1 0 11 3p 2(1) + = 3 1, 0, -1 32 3d 2(2) + = 5 2, 1, 0, -1, -2 5
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ELECTRON SPIN QUANTUM NUMBER (ms)
• Describes the spin direction of an electron. There are only two possible values for the electron spin quantum number, and these are + ½ and – ½.
• ms = + ½ (clockwise)
• ms = - ½ (counter-clockwise)
+N
N
+
n=1n=2n=3
n= so on…
K L M
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ELECTRON CONFIGURATION
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PAULI’S EXCLUSION PRINCIPLE• Wolfgang Pauli• States that no two electron can be described by the
same four quantum numbers. • Two electrons may have the same first three quantum
numbers (n, l, ml) but these two electrons must
have different spins (ms).
• Pauli’s exclusion principle implies that each orbital in an atom can hold at most two electrons and that two electrons must have opposite spin.
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THE AUFBAU PRINCIPLE• Principle applies the laws in QUANTUM MECHANICS to
the distribution of electrons among energy levels in the ground states (most stable states) of atoms.
• The word AUFBAU means “building up” in german.
• The principle describes a hypothetical process in which the electrons are imagined as entering the atomic orbitals one by one. The process results in obtaining the electron configuration of an atom in its ground state.
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Electron Filling Order
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5s
4s
3s
2s
1s
2p
3p
4p
3d
4dE
N
E
R
G
Y
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Writing Atomic Electron Configurations
11 s
value of nvalue of l
# of e
spdf notationfor H, atomic # = 1
2 ways of writing
configs. One is
called the spdf
notation.
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Other is called the orbital box notation.
Arrowsdepictelectronspin
ORBITAL BOX NOTATIONfor He, atomic number = 2
1s
21 s
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Relation between orbital filling & the periodic table
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Electron Arrangement in Atoms
Electron Arrangement in Atoms
Electrons in atoms are arranged as:
SHELLS (n)
SUBSHELLS (l)
ORBITALS (ml)