10112011 page 1
Bohr Model
In 1913 Niels Bohr proposed a model for the
HYDROGEN ATOM
1 positive proton and 1 negative electron.
Hydrogen emission spectra are always the same– the electron doesn’t spiral into the proton and form a neutral particle.
BOHR MODEL: The electron can only move in fixed,
CIRCULAR ORBITS
e- must
be in a fixed
orbit.
n = 1
n = 2
n = 3
Bohr’s Results (cont.)
The energy of an electron in an atom is –
En = - 2.18 X 10-18 J/ n2
where n = 1, 2, 3, 4, ......
n is the quantum number
RESULTING ENERGY LEVELS:
Ground State = lowest available energy
For hydrogen this is 1 e’ in the n=1 level
Excited State = when e’ is in a higher level
Bohr’s Model successfully predicted the atomic emission lines for hydrogen-
656 nm 486 nm 434 nm 410 nm
Calculated values exactly as observed
PROBLEM: This worked well for
Hydrogen it did not work for larger atoms like
Helium and Lithium!
Something was wrong with the model!
Wave Mechanical Model
Louis deBroglie (1924) –
Light is sometimes wave, sometimes particle
Perhaps the electron also has a dual nature!
Equation linking wave and particle behavior
for matter: “Bridge Equation”
momentum
wave behavior particle behavior
= wavelength of particle`
h = Planck’s Constant
m = mass of particle
v = velocity of particle
(careful! don’t confuse v with frequency, )
Confirmed by fact that a beam of electrons can be diffracted(show wave behavior) in the same way emr does!
Heisenberg Uncertainty Principle- it is impossible to know both the velocity and the location of an electron.
(the act of observing it affects an electron!)
WAVE MECHANICAL MODEL
WAVE EQUATION-
Developed by Erwin Schrodinger to consider electrons as waves as well as particles.
H = E
H is the energy operator
E is the energy
is the state function
The state function gives a
probability distribution
ATOMIC ORBITAL – the probability distribution for where an electron will be found in the atom.
ENERGY VALUES – definite, quantized values are the only possible energies an electron in the atom can have.
Wave Mechanical Results for Hydrogen
En = -2.18 X 10-18 J/ n2
where, n = 1, 2, 3, …….
This is in exact agreement with
experimental observations.
Same as Bohr model- Is that good or bad?
ATOMIC ORBITALS (not orbits!) provide a new understanding of the atom.
What’s the difference between an orbital and an orbit?
answer: An orbit is a fixed track. An orbital is a probability distribution.
Quantum Wave Mechanics
Results for Hydrogen Atom
n = principal quantum number
En = value for Principal Energy Level
Each Principal Energy Level contains sublevels.
Level Number of Label(s)
sublevels
n = 1 1 s
n = 2 2 s and p
n = 3 3 s, p and d
n = 4 4 s, p, d, and f
How many sublevels are there in principal energy levels with n =5 and 6?
Sublevels are characterized by specific atomic orbitals (AO’s)
Sublevel Orbital Shape Orbital
s spherical s
p “dumbbell” px, py, pz
d “4-lobes” 5 different
d orbitals
(See figs 5-15 and 5-16 on p 133 in book.)
AO’s in the Principal Levels
Principal Level n=1 contains
a single 1s AO
Principal Level n=2 contains
a 2s AO and a set of 2p AO’s
2px, 2py, and 2pz
(p AO’s come in sets of 3)
Principal Level n=3 contains
a 3s AO ; a set of 3p AO’s; and-
a set of 3d AO’s
(d AO’s come in sets of 5)
3dxy, 3dxz, 3dyz, 3dx2-y2, and 3dz2
Principal Level n=4 contains
one 4s, three 4p, five 4d,
and seven 4f AO’s
General Rule:
An Atomic Orbital (AO) can hold
up to 2 e’s.