the bohr model; wave mechanics and orbitals
DESCRIPTION
The Bohr Model; Wave Mechanics and Orbitals. Bohr’s Quantum Model of the Atom. Attempt to explain H line emission spectrum Why lines ? Why the particular pattern of lines? Emission lines suggest quantized E states…. nucleus. ( ). E n = -2.18 x 10 -18 J. 1. n 2. - PowerPoint PPT PresentationTRANSCRIPT
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The Bohr Model; Wave Mechanics and Orbitals
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Attempt to explain H line emission spectrum Why lines? Why the particular pattern of lines? Emission lines suggest quantized E states…
Bohr’s Quantum Model of the Atom
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e- occupies only certain quantized energy states
e- orbits the nucleus in a fixed radius circular path
Ee- in the nth state
depends on Coulombic attraction of nucleus(+) and e-(-)
always negative
Bohr’s Model of the H Atom
En = -2.18 x 10-18 J ( )1n2 n = 1,2,3,…
nucleus
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First Four e- Energy Levels in Bohr Model
n=1
n=2n=3
n=4
nucleusn=3
n=2
n=1
E
ground state
excited states
n=4
E Levels are spaced increasingly closer together as n
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En = -2.18 x 10-18 J ( )1n2
n = 1,2,3,…
Energy of H atom e- in n=1 state?
In J/atom: En=1 = -2.18 x 10-18 J/(12) = -2.18 x 10-18 J/atom
In J/mole: En=1 = -2.18 x 10-18 J/atom(6.02 x 1023 atoms/mol)(1kJ/1000J) = -1310kJ/mol
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n=1
n=2n=3
n=4
n=3
n=2
n=1
E
-2.42 x 10-19 J/atom
-5.45 x 10-19 J/atom
-2.18 x 10-18 J/atom
n=4 -1.36 x 10-19 J/atom
First Four e- Energy Levels in Bohr Model
the more - , the lower the En
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n=1
n=2n=3
n=4
n=3
n=2
n=1
E
-2.42 x 10-19 J/atom
-5.45 x 10-19 J/atom
-2.18 x 10-18 J/atom
n=4 -1.36 x 10-19 J/atom
What is E for e- transition from n=4 to n=1? (Problem 1)
E = En=1 - En=4 = -2.18 x 10-18J/atom - (-1.36 x 10-19J/atom) = -2.04 x 10-18J/atom
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What is of photon released when e- moves from n=4 to n=1? (Problem 1)
Ephoton = |E| = hc/
2.04 x 10-18J/atom = (6.63 x 10-34 J•s/photon)(3.00 x 108 m/s)/
= 9.75 x 10-8 m or 97.5 nm A line at 97.5 nm (UV region) is
observed in H emission spectrum.
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Bohr Model Explains H Emission Spectrum
En calculated by Bohr’s eqn predicts all ’s (lines).
Quantum theory explains the behavior of e- in H.
But, the model fails when applied to any multielectron atom or ion.
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Wave Mechanics
Quantum, Part II
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Wave Mechanics Incorporates Planck’s quantum theory
But very different from Bohr Model
Important ideas Wave-particle duality Heisenberg’s uncertainty principle
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Wave-Particle Duality e- can have both particle and wave properties
Particle: e- has mass Wave: e- can be diffracted like light waves
e- or light wave
wave split into pattern
slit
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h/mu
u = velocity m = mass
Wave-Particle Duality Mathematical expression (deBroglie)
Any particle has a but wavelike properties are observed only for very small mass particles
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Heisenberg’s Uncertainty Principle Cannot simultaneously measure position (x) and
momentum (p) of a small particle
x . p > h/4 x = uncertainty in position p = uncertainty in momentum
p = mu, so p E
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Heisenberg’s Uncertainty Principle
As p 0, x becomes large
In other words, If E (or p) of e- is specified, there is large
uncertainty in its position Unlike Bohr Model
x . p > h/4
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Wave Mechanics(Schrodinger)
Wave mechanics = deBroglie + Heisenberg + wave eqns from physics
Leads to series of solutions (wavefunctions, ) describing allowed En of the e-
n corresponds to specific En Defines shape/volume (orbital) where e- with En is likely to be
n gives probability of finding e- in a particular space
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probability density falls off rapidlyas distance from nucleus increases
Where 90% of thee- density is foundfor the 1s orbital
Ways to Represent Orbitals (1s)
1s
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Quantum Numbers
Q# = conditions under which ncan be solved
Bohr Model uses a single Q# (n) to describe an orbit
Wave mechanics uses three Q# (n, l, ml) to describe an orbital
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Three Q#s Act As Orbital ‘Zip Code’
n = e- shell (principal E level)
l = e- subshell or orbital type (shape)
ml = particular orbital within the subshell (orientation)
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l = 0 (s orbitals)
l = 1 (p orbitals)
these have different ml values
Orbital Shapes
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these have different ml values
l = 2 (d orbitals)
Orbital Shapes
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Energy of orbitals in a 1 e- atom
Three quantum numbers (n, l, ml) fully describe each orbital.
The ml distinguishes orbitals of the same type.
n=1
n=2
n=3
E
1s
2s 2p
3p 3d3s
orbitall = 0 l = 1 l = 2
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Spin Quantum Number, ms
In any sample of atoms, some e- interact one way with magnetic field and others interact another way.
Behavior explained by assuming e- is a spinning charge
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ms = -1/2ms = +1/2
Spin Quantum Number, ms
Each orbital (described by n, l, ml) can contain a maximum of two e-, each with a different spin.
Each e- is described by four quantum numbers (n, l, ml , ms).
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Energy of orbitals in a 1 e- atom
E
1s
2s 2p
3p 3d3s
orbital
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Filling Order of Orbitals in Multielectron Atoms
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The Quantum Periodic Table
l = 0 l = 2l = 1
l = 3
n
1
2
3
4
5
6
7
67
s blockd block
p block
f block
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More About Orbitals and Quantum Numbers
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n = principal Q#
n = 1,2,3,… Two or more e- may have same n value
e- are in the same shell n =1: e- in 1st shell; n = 2: e- in 2nd shell; ...
Defines orbital E and diameter
n=1
n=2n=3
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l = angular momentum or azimuthal Q#
l = 0, 1, 2, 3, … (n-1) Defines orbital shape # possible values determines how many orbital
types (subshells) are present Values of l are usually coded
l = 0: s orbitall = 1: p orbitall = 2: d orbitall = 3: f orbital
A subshell l = 1 is a ‘p subshell’An orbital in that subshell is a ‘p orbital.’
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ml = magnetic Q#
ml = +l to -l Describes orbital orientation # possible ml values for a particular l tells how
many orbitals of type l are in that subshell
If l = 2 then ml = +2, +1, 0, -1, -2
So there are five orbitals in the d (l=2) subshell
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Problem: What orbitals are present in n=1 level? In the n=2 level?
n(l)1s one of these
2s one2p three
If n = 1 l = 0 (one orbital type, s orbital) ml = 0 (one orbital of this type) Orbital labeled 1s
If n = 2 l = 0 or 1 (two orbital types, s and p)
for l = 0, ml = 0 (one s orbital)
for l = 1, ml = -1, 0, +1 (three p orbitals)
Orbitals labeled 2s and 2p
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Problem: What orbitals are present in n=3 level?
If n = 3 l = 0, 1, or 2 (three types of orbitals, s, p,and d)
l = 0, s orbital l = 1, p orbital l = 2, d orbital
ml for l = 0, ml = 0 (one s orbital)
for l = 1, ml = -1, 0, +1 (three p orbitals)
for l = 2, ml = -2, -1, 0, +1, +2 (five d orbitals)
Orbitals labeled 3s, 3p, and 3d
n(l)3s one of these
3p three 3d five
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Problem: What orbitals are in the n=4 level?
Solution One s orbital Three p orbitals Five d orbitals Seven f orbitals