Download E = mc2 m = hc λc2 = h λc h λ= mv h λ= mc

Important Equations
 c = λν
c = 3 x 108 m per second
λ = wavelength
ν = frequency
hc
Ephoton = h ν =
λ
 E = hν
h = Planck’s constant = 6.62 x 10-34 J s
or
h = 6.62 x 10-34 kg m2 s-1
Week 5
CHEM 1310 - Sections L and M
1
“Quantum”
 Light is quantized [Max Planck, 1901]
– Quite a surprise as light was thought to be continuous
 Energy can be gained or lost only in integer multiples
of h ν.
ΔE = n(h ν)
n is an integer (1,2,3,…)
 Each unit of size hν is called a packet or quantum
Week 5
CHEM 1310 - Sections L and M
2
Energy Has Mass!
E = mc2
m=
E
c2
Êcˆ
E = hn = hÁ ˜
Ë l¯
Week 5
m=
hc
λ c2
λ=
λ=
CHEM 1310 - Sections L and M
=
h
λc
h
mc
h
mv
3
1
Hydrogen’s Atomic Spectrum
Week 5
CHEM 1310 - Sections L and M
4
Light & Energy Are Quantized
DE n =
hc
ln
n is excited state orbitals
n = 1, 2, 3, …
Week 5
CHEM 1310 - Sections L and M
5
Bohr Model
Discrete energy levels
available to electrons
in which to move
Week 5
CHEM 1310 - Sections L and M
Niels Bohr
(1885-1962 )
Nobel Prize
Physics,
1922
6
2
Bohr Model
Another
View
Week 5
Niels Bohr
(1885-1962 )
Nobel Prize
Physics,
1922
CHEM 1310 - Sections L and M
7
What Bohr’s Calculations Led To
Angular
momentum,
radius, and
energy of the
electrons
traveling in
discrete orbits
Angular Momentum = mevr
h
= n
n = 1,2,3,.....
2p
Week 5
Z2
E n = - 2 (2.18x10-18 J)
n
n2
a 0 = radius of each orbital
Z
a 0 called the bohr radius, a constant
rn =
n = orbitals, excited states
n = 1,2,3,...
n = 1 called ground state
Z is the postive charge on the nucleus
(1 of H, 2 for He, etc.)
CHEM 1310 - Sections L and M
8
Heisenberg Uncertainty Principle
Dx ! mDv "
n
4p
imprecision of
position
imprecision of momentum
Werner Heisenberg
1927
You cannot measure/observe something without changing
that which you are observing/measuring.
Week 5
CHEM 1310 - Sections L and M
9
3
Schrödinger Equation
Ĥψ= Eψ
Ĥ is a Hamiltonian operator in linear algebra
E = total energy of the atom
ψ= a wave function which defines an electrons
position in 3D space (x, y, z), called an orbital
ψ2 = the probability that an electron is in a certain
region of space; this defines the shape of the orbital
(s, p, d, f)
Week 5
CHEM 1310 - Sections L and M
10
Movement of an Electron
The H e- can be visualized as a standing wave
around the nucleus.
Not the planetary orbits assumed by Bohr.
Week 5
CHEM 1310 - Sections L and M
11
Solutions to the Schrödinger Eqn
1. n = principal quantum number
ψ(n, l, ml)
n = 1, 2, 3, …
n is related to the size and energy of the orbital
2. l = angular (azimuthal) quantum number
l = 0, 1, …. (n-1)
l is related to the shape of the orbital
l = 0 is called an s orbital
l = 1 is called a p orbital
ψ(n,
l = 2 is called a d orbital
l = 3 is called an f orbital
l = 4 is called a g orbital
Week 5
CHEM 1310 - Sections L and M
l, ml)
12
4
Solutions to the Schrödinger Eqn
3. ml = magnetic quantum number
ml = -l, … , 0, ….+l
ψ(n, l, ml)
ml relates to the orientation of the orbital
4. Although not a solution to the
Schrödinger Equation, a 4th quantum
number is
ms = electron spin quantum number
ms = +1/2, -1/2 denoted by ↑↓
Week 5
CHEM 1310 - Sections L and M
13
Hydrogen Atom
– n is related to the size and energy of the orbital
– l is related to the shape of the orbital
– ml relates to the orientation of the orbital
n
l
orbital
designation
ml
# of
orbitals
1
0
0
1
0
1
2
0
1
2
3
1s
2s
2p
3s
3p
3d
4s
4p
4d
4f
0
0
-1, 0, +1
0
-1, 0, +1
-2, -1, 0, +1, +2
0
-1, 0, +1
-2, -1, 0, +1, +2
-3, -2, -1, 0, +1, +2, +3
1
1
3
1
3
5
1
3
5
7
2
3
4
Week 5
CHEM 1310 - Sections L and M
14
Representations of Orbitals
ψ(1, 0, 0)
Week 5
ψ(2, 0, 0)
ψ(3, 0, 0)
CHEM 1310 - Sections L and M
15
5
Representations of p-Orbitals
Week 5
CHEM 1310 - Sections L and M
16
Representations of d-Orbitals
Week 5
CHEM 1310 - Sections L and M
17
6