1/9/2020 1 Chemistry is all around us Everything you hear, see, smell, taste, and touch involves chemistry and chemicals (matter). And hearing, seeing, tasting, and touching all involve intricate series of chemical reactions and interactions in your body…(acs.org) In more formal terms chemistry is the study of matter and the changes it can undergo. What is matter?
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1/9/2020
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Chemistry is all around us
Everything you hear, see, smell, taste, and touch involves chemistry and chemicals (matter).
And hearing, seeing, tasting, and touching all involve intricate series of chemical reactions and interactions in
your body…(acs.org)
In more formal terms chemistry is the study of matter and the changes it can undergo.
What is matter?
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What is matter composed of?
What are atoms made of?
What are protons, neutrons, and electrons made of?
Democritus (c. 460–c. 370 B.C.) proposed that matter was made of discrete indivisible particles. He called his particles atomon,
meaning "cannot be cut."
His ideas were largely ignored until the scientific revolution of
the 16th, 17th, and 18th centuries.
The Atom
Lavoisier 1774 - Law of conservation of mass:The total mass of substances present after a chemical reaction is the same as the total mass of substances before the reaction
Proust 1799 - Law of definite proportions:All samples of a compound have the same composition-the same proportions by mass of the constituent elements.
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Conservation of Mass
Each element is composed of small particles called atoms.
Atoms are neither created nor destroyedin chemical reactions.
All atoms of a given element are identical.
Compounds are formed when atoms of more than one elementcombine.
Dalton’s Atomic Theory
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While atoms were thought to be indivisible, that all changed when J(oseph) J(ohn) Thomson (1856–1940) discovered the electron in 1897.
Ernest Rutherford (1871–1937) showed that the electrons occupied a region of space surrounding the tiny nucleus.
Figuring out just how those electrons behaved required the development of quantum mechanics, a theory in which electrons are treated as wavelike.
Radioactivity
Radioactivity is the spontaneous emission of radiation from a substance.
X-rays and g-rays are high-energy light.
a-particles are a stream of helium nuclei,
He2+.
b-particles are a stream of high speed
electrons that originate in the nucleus.
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2-3 The Nuclear Atom
Geiger and Rutherford1909
The a-particle experiment
Most of the mass and all of the positive charge is concentrated in a small region called the nucleus .
There are as many electrons outside the nucleus as there are units of positive charge on the nucleus
Where E is the energy of the atom, is called a wave function and H is the Hamiltonian operator
The complete form of the Schrödinger equation:
),,(),,(),,(8 2
2
2
2
2
2
2
2
zyxEzyxzyxVdz
d
dy
d
dx
d
m
h
e
The complete form of the Schrödinger equation:
),,(),,(4
sin
1
sin
11
2
0
2
2
2
22
2
2
2
2
2
rErr
e
rr
rrr
rr
n
– wavefunction Me – electron’s mass
E – total quantized energy V – potential energy of point (x, y, z)
In Cartesian coordinates
In Spherical coordinates
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0
r
y
x
z
z
y
x
Cartesian coordinates Spherical coordinates
N
Potential energy of an electron (attraction between the e- and the nucleus).
Kinetic energy of an electron (the energy of the moving e-).
Wave properties of an e-.
What is included in the Schrödinger equation?
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),,(),,(4
sin
1
sin
11
2
0
2
2
2
22
2
2
2
2
2
rErr
e
rr
rrr
rr
n
Focus on the solutions
The solutions to the Schrödinger equation answer
the following questions:
What is the energy of the electron?
Where is the electron most likely to exist?
The probability of finding the electron (electron density).
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),()(),,( YrRr
Wavefunction Radial part
(how far?)
Angular part
(Where?)
We don’t care where the electron is.
We want to know how far it is away from the nucleus.
1 for an s orbital
),,( rFirst low energy solution
e
a
zR s
23
0
1 2
Exponential Decay
Don’t worry about where this comes from.
Constants
z – the charge on the nucleus (1 for hydrogen)
a0 – the Bohr radius ≈ 0.53Å
σ = zr/a0
The farther from the nucleus, the lower the likelihood of finding the electron.
21s
r
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Figure 7.16Electron probability in the ground-state H atom.
Figures A and B - Electron density (probability of finding e- at a single point) vs. radius for the 1s orbital
2
1
24 sRr
Bohr radius≈
0.53Å
Higher e-
density
Lower e-
density
The 1s orbital is represented by drawing a sphere about nucleus within which e- spends 90% of its time, 90% probability contour.
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2
23
0
2 222
1
e
a
zR s
If σ = 2, then this term
goes to zero and ψ2 goes
to zero.
Somewhere there is a node, the electron
cannot be found at this
radius.
N
Potential energy of an electron (attraction between the e- and the nucleus).
Kinetic energy of an electron (the energy of the moving e-).
Wave properties of an e-.
What is included in the Schrödinger equation?
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Orbital – region of space where the e- is likely to be foundDifferent orbitals have different sizes, shapes and orientationsEach orbital is identified by 3 quantum numbers (n, l, ml)
n = principal quantum no. = 1, 2, 3, etc.determines energy and size of orbital n = 1is lowest energy and smallest size
l = angular momentum quantum no. = 0, 1, 2, . . ., (n – 1)determines shape of orbital
ml = magnetic quantum no. = -l … 0 … +l(integers, determines orientation of orbital)
n=1
n=2 n=2
n=3 n=3
n=4 n=4
n=5 n=5n=6 n=6
h
h
h
h
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l Shape of orbital
0 s
1 p
2 d
3 f
Total no. orbitals/shell = n2
n l ml No. of
orbitals
Sublevel
1 0 0 1 1s
2 0 0 1 2s
1 +1,0,-1 3 2p
3 0 0 1 3s
1 +1,0,-1 3 3p
2 +2,+1,0,-1,-2 5 3d
4 0 0 1 4s
1 +1,0,-1 3 4p
2 +2,+1,0,-1,-2 5 4d
3 +3,+2,+1,0,-1,-2,-3 7 4f
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Figure 7.17
1s 2s
Radial probability plot – 1 peak for the 1s, 2
peaks for the 2s.
2s orbital is also spherical, but it
contains 2 layers.
3s
Radial probability plot –3 peaks for
the 3s.
The 3s orbital contains 3 layers.
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),()(),,( YrRr
Wavefunction Radial part
(how far?)
Angular part
(Where?)
If not one, what is the shape?
cos4
3
sinsin4
3
cossin4
31
4
10
21
21
21
21
Pz
Py
Px
s
Y
Y
Yl
Yl
Angular part describes the
shape.
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Figure 7.18
The 2p orbitals.
Lowest energy p orbital, 2p, has a single peak in the radial probability plot.
Single peak slightly closer to the nucleus than the larger peak in the 2s plot.
Figure 8.5
Figure 7.18The 2p orbitals.
Three 2p orbitals shapes.
Each orbital centered along different axis (x, y, z)
Px, Py, Pz
2Pz orbital, e- wave has no amplitude on the xy plane, called a nodal plane
Three 2p orbitals, as far apart as possible
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H atoms, and only H, 2s and 2p have same energy
Energy depends only on n.
In the 3p orbital, the e- spends the most time outside the 2p region, but some time in the 2p region.
In the third shell, there is two peaks on the radial probability plot.