Transcript Early Quantum Theory and Models of the Atom

27-12 The Bohr Model
• Bohr studied Rutherford’s planetary model and
found it had validity
• But to make it work the newly developing
quantum theory would have to be incorporated
• Plank and Einstein had shown that in heated
solids, the energy of oscillating electric charges
must change from one discrete energy state to
another with the emission of a quantum of light
• Whole steps, not continuous
• Bohr argued that the electrons in a
atom also couldn’t lose energy
continuously, but must do so in
quantum “jumps”
• Bohr assumed that the electrons move
about in a certain circular orbit
• Each orbit have a specific amount of
energy
• The electrons could move about in that
orbit without radiating energy
• He called the possible orbits stationary
states
• Light is emitted only when an electron
jumps from a higher energy state to a
lower energy state
• When the “jump” happens a single
photon of light is emitted whose energy
is the difference between the two states
• Bohr found that his theory was in line
with the Balmer formula is he assumed
that the electron’s angular momentum
is quantized
• His resulting equation didn’t have firm
theoretical foundation
• He searched for some quantum
condition and ties to E=hf
• But is didn’t give the desired results
• His reason for using his equation was
that it worked
• His equation is explained by using
Coulomb’s law, Newton’s law and much
substitution
• results
2 Z e mk 1
En  
2
2
h
n
2
2 4
2
Where E is the energy level
n is the orbit
Z is the number of positive charge
e is the charge of an electron
m is the mass of an electron
k is Coulomb’s law constant
h is Planck’s constant
• Or converted to eV
• The lowest energy level for hydrogen is
-13.6eV
2
Z
En  (13.6eV ) 2
n
• So both the orbit radii and the energy
levels are quantized
• The quantum number, n, labels the
orbit radii and the energy levels
• The lowest energy level is called the
ground state
• The higher energies levels are called
excited states
• The farther the energy levels are from
the nucleus the higher the energy
• The minimum energy required to
remove an electron from the ground
state is called the binding energy
• Hydrogen is 13.6 eV
• Corresponds to removing an electron
from the lowest state to where it is free
and E=0
• Once in an excited state an atom’s
electron can jump down to a lower state
and give off a photon in the process
• This is the origin of the emission spectra
of excited gases
• The vertical arrows represent the
transitions or jumps that correspond to
the various observed spectral lines
The lowest energy level
is called the ground
state; the others are
excited states.
• The success of Bohr’s model it can
explain why atoms emit line spectra and
correctly predicts the wavelengths or
emitted light for hydrogen
• The Bohr model can also explain
absorption spectra
• Photons of just the right wavelength
can knock an electron from one energy
level to a higher one
• To conserve energy, only photons that
have the right energy will be absorbed
• Bohr model also guarantees the stability
of the atoms
• Bohr model is great for finding the
binding energy of hydrogen, but not for
other atoms
• Bohr model was a very important start
• The concepts of stationary states, the
ground state, and the transitions
between states are still used today
Correspondence Principle
• Bohr made radical assumptions to make
his model work
• Electrons in fixed orbits don’t radiate
light
• Was unable to say how electrons were
raised to a higher energy level
• No real reason why a tiny electron
would behave like a regular sized object
• The correspondence principle can predict
classical results by overlapping the
quantum theory with the macroscopic
world
• His theory does work for hydrogen with
n=1, but not very well for n=100,000,000
• The well defined orbits defined by the
Bohr model don’t really exist
• This idea rejected a few years after Bohr
proposed it
• Today electrons for “probability clouds”
27-13 de Broglie’s Hypothesis
• Bohr’s theory was based on assumptions that
were made to have the theory agree with
experiments
• Bohr could give no reason why orbits were
quantized
• 10 years later Louis de Broglie proposed that all
particles have wave nature
• One of de Broglie’s original arguments
supporting the wave nature of electrons was to
provide an explanation of Bohr’s theory
• De Broglie hypothesized that electrons
have a wavelength
• The orbits correspond to circular
standing waves in which the
circumference of the orbit equals whole
number of wavelengths
• Bohr’s theory worked well for hydrogen,
but wasn’t successful for multi-electron
atoms
• A new theory was developed in the
1920s called quantum mechanics
• The electrons being in a well defined
orbit was replaced with electron
“clouds”