Download Models of the Atom

Models of the Atom
Rutherford, Bohr, De Broglie and
Quantum Physics
Nature of Electrons
Originally called cathode rays
Reversing magnet shows that they are
charged particles
Plum Pudding Model
(Thompson - 1890’s)
Positively
charged
material
Rutherford Experiment (1911)
Alpha Particle is 2n2p
or helium nucleus
Another View
Results of Rutherford
Experiment
Most alpha particles pass through
undeflected
Conclusion: atom is mostly empty space
Some deflected at very large angles,
even backward
Conclusion:positive charge is
concentrated in a small region of atom
Animation
Rutherford’s Planetary Model
of Hydrogen Atom
Size of nucleus =
10-15 m
Size of atom =
10-10 m
Two problems
Stability
Continuous spectrum not seen
Atomic Spectra
Observe with gas discharge tube
Glow due to accelerated
electrons striking atoms in low
pressure gas and exciting them
Light from tube found to
contain discrete wavelengths
Spectrometer Set Up
Emission Spectrum
Use diffraction grating or prism
spectrometer to see
Compare to white light
spectrum(continuous)
Graphics courtesy of Science
Joy Wagon Physics Zone
Shows visible portion
of spectrum
Divide by 10 to get
nanometers
A high school teacher
named Balmer found
that these
wavelengths obeyed
a 1/n2 rule
Infra-red
Visible
Shows Energy of emitted photons
UV
One Formula Fits All
(but no one knew why it worked)
Each observed wavelength
described by
1/l = R (1/n’2 – 1/n2)
n’ = 1 for Lyman, n’ = 2 for Balmer,
n’ = 3 for Paschen
R = Rydberg Constant = 1.097 x 10^7
m^-1
Rutherford Model Could Not
Explain…
Why atoms emit line spectra
Why atom is stable. Accelerated
electrons should emit radiation with
increasing frequency as they spiral into
atom.
Spectra should be continuous.
Bohr Model
Atom has discrete energy levels - states
Electrons move in orbits without
radiating energy
Light quanta (photons) emitted when
electrons jump from state to state
hf = Eu - El
Eu
hf
El
Bohr – Balmer Connection
Bohr’s theory agrees with Balmer if
electron angular momentum quantized
L = mvrn = n h/2p
n = 1, 2, 3, …
rn is radius of nth possible orbit
Bohr Theory for Hydrogen
Atom
Electron and Nucleus held together by
Coulomb force
Predicts r1 = 0.529 x 10-10 m as radius of
smallest oribit in hydrogen (Bohr Radius)
Leads to Lyman, Balmer, Paschen formulae
En = -13.6 eV/n2
Ground state has most negative energy
Excited states have higher(more positive)
energy
Bohr’s Derivation
F = ma
kZe2/ (rn) 2 = mv2 /rn
Mvrn =nh/2p
rn = n2h2/(4p2mkZe2)
En= ½ mv2 – kZe2/rn = -2p2Z2e4mk2/n2h2
En = - 13.6/n2
Bohr Radii
Ground state has smallest radius
Excited states have larger radii
r = n2 r1
Changes in level are
called atomic transitions
Bohr Energy Levels for
Hydrogen Atom
n
En = -13.6
eV/n2
1
-13.6 eV
2
-3.40 eV
3
-1.51 eV
4
-0.85 eV
Ionized atom, positive continuous energies, electron free
E=0
E= -1.5 eV
E = -3.4 eV
E=-13.6 eV
Ground state
Emission vs. Absorption of
Photon Energy
Emission- atom drops to lower states

Random and spontaneous process
Absorption – atom rises to higher
states. Only photons of just the right
energy can be absorbed
Question: If you shine a light on
a gas do you get
Absorption?
Emission?
Both?
Ionization Energy
Minimum energy to kick electron out of
ground state
13.6 eV for hydrogen atom
Can supplied by heating or collision
Find the Wavelength
What is the wavelength in the transition
from n=2 to n=1?
hf = E2 – E1 = 13.6 eV – 3.40 eV = 10.2 eV
l = c/f = hc/(E2 – E1) = (6.63x10-34 J-S)(3.00x108
m/s)/(10.2 eV)(1.6 x 10-19 J/eV) =
= 1.22 x 10-7 m or 122 nm
What kind of light is this?
Ans. Ultra Violet
De Broglie Waves in Atoms
Why should orbits be quantized a la
Bohr?
De Broglie; wave is associated with
electron l = h/mv
Only orbits that correspond to standing
waves can persist
Circumference must contain whole
number of wavelengths
Standing Circular Waves
2prn = nl n = 1, 2, 3
But l = h/mv
2prn = nh/mv
or mvrn = nh/2p
This was Bohr’s quantization condition
Implies wave-particle duality at root of
atomic structure
Limitations of Bohr Theory
Could not explain spectra of other than
hydrogen atoms
Could not explain why emission lines
are double, triple or more
Could not explain why some lines
brighter than others
Could not explain how atoms bond
Mixed classical and quantum ideas
Quantum Mechanics
Next step after Bohr in explaining atomic
physics
Explains details of spectra
Gives classical(correct) results for larger
objects
Based on “Wave functions,” probability and
Schrodinger equation
Modern theory called “quantum
electrodynamics.”
Heisenberg Uncertainty
Principle
Accuracy of some measurements is inherently
limited by nature
To observe is to interfere
We cannot measure the momentum and
position of an object precisely at the same
time
The energy of an object may be uncertain(or
even non-conserved) for a small time
Probability vs Determinism
On sub-atomic scale nature is
probabilistic not deterministic
Certain paths and events knowable only
in terms of probability
Electrons form cloud around atom
called probability distribution
Quantum Numbers Determine
State of Atom
Principle quantum number-from Bohr
theory
Orbital quantum number-related to
angular momentum
Magnetic quantum number-related to
direction of electron’s angular
momentum
Spin quantum number
Pauli Exclusion Principle
No two electrons in an atom can occupy
the same state
Can’t have exactly the same quantum
numbers
Helps determine patterns of regularities
in Periodic Table of Elements(explained
by quantum mechanics)