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Transcript
Bohr’s atomic model
Chapter 2, Atomic Physics
 Four puzzles




Blackbody radiation
The photoelectric effect
Compton effect
Atomic spectra
 Balmer formula
 Bohr’s model
 Frank-Hertz experiment
Nankai University, CY Li
2017/5/24
1
Chapter 2, Atomic Physics
Some words
 Blackbody
 Discrete spectra
 Absorb, emit
 Rydberg constant
 Spectrum
 orbital angular
 Ultraviolet
momenta
 quantum number
 quantum mechanics




catastrophe
Incident
photoelectric effect
Frequency
Compton effect
Nankai University, CY Li
2017/5/24
2
Chapter 2, Atomic Physics
Blackbody
 Thermal radiation: electromagnetic radiation
emitted by hot objects, at room temperature?
 Absorptivity (absorptance): the ratio of the
radiation absorbed by a body to that incident
on the body.
 Blackbody: A body with a surface having an
absorptivity equal to unity.
 A realistic blackbody: For a cavity kept at a
constant temperature with the interior wall
blackened, a small hole in the wall behaves
like a blackbody.
Nankai University, CY Li
2017/5/24
3
Chapter 2, Atomic Physics
Some observations
 Stefan's Law states that the power radiated by
a body is proportional to the 4th power of the
absolute temperature. R  T 4
 For a given temperature, the radiation forms a
continuous spectrum with respect to the
frequency.
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2017/5/24
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Chapter 2, Atomic Physics
Wein's Displacement Law
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2017/5/24
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Chapter 2, Atomic Physics
Reyleigh-Jeans law
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2017/5/24
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Chapter 2, Atomic Physics
Ultraviolet catastrophe
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2017/5/24
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Chapter 2, Atomic Physics
Puzzles in blackbody radiation
 Two puzzles:


Why were not radiation above the ultraviolet
region present?
Why was there a non-uniform distribution of
electromagnetic radiation being emitted?
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2017/5/24
8
Chapter 2, Atomic Physics
Plank’s theory
 Planck made an assumption that the energy of
an oscillator must be an integral multiple of the
product of the constant h and the frequency of
the electromagnetic radiation it emitted.
E0  nhf
 His assumption resulted in a formula for the
blackbody radiation that was in excellent
agreement with experiment at all frequencies.
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2017/5/24
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Chapter 2, Atomic Physics
Two puzzles to be explained
 Radiation in the high frequency region were
not emitted from the blackbodies because
this required large energy changes which
could not occur in the atoms.
 Certain energy states were more probable
in the atoms and therefore frequencies
associated with these energy states were
more likely to be emitted.
Nankai University, CY Li
2017/5/24
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Chapter 2, Atomic Physics
The photoelectric effect
 When light of a high frequency was incident on a
metallic surface, electrons were emitted from the
surface.
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2017/5/24
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Chapter 2, Atomic Physics
Actual observation
 Intensity: The high intensity of light would not
cause electrons to have high KE. The actual
reaction time is very short (10-9s).
 Frequency: At a certain frequency called threshold
frequency, electrons were emitted. A frequency
beyond it will cause the electrons to have a
greater KE.
 Stopping voltage: The energy of the ejected
electrons was proportional to the frequency of the
illuminating light & had nothing to do with intensity.
Nankai University, CY Li
2017/5/24
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Chapter 2, Atomic Physics
Einstein’s explanation
 For a photoelectron, E=hf .
 The minimum energy required to pull
electrons from inside to outside the metal is
called the work function W. W=hf0
 If an electron is given an energy E larger
than W, it can escape the metal and will
have a maximum KE:
1 2
mvmax  E  W  hf  hf 0
2
Nankai University, CY Li
2017/5/24
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Chapter 2, Atomic Physics
The Compton effect
(Compton scattering)
 This could be
 f  i   
2h

sin 2
me c
2
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explained when X
rays are regards as
particles (photons).
The collision
between a photon
and an electron is
regarded as an
elastic collision.
2017/5/24
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Chapter 2, Atomic Physics
Discrete spectra
 Atoms emit and absorb light only at specific
frequencies.


Emission lines,
Absorption lines,
 Balmer found that the wavelengths of visible and
near ultraviolet line spectra of hydrogen obey a
simple formula exactly:
1
1 1
 RH ( 2  2 )

2 n
 RH=1.097x107m-1 is called the Rydberg (里德伯)
constant.
Nankai University, CY Li
2017/5/24
15
Chapter 2, Atomic Physics
Bohr model
 There are three postulates used in Bohr’s
model:



The electron moved in a certain set of stable orbits in
which classical mechanics can be used to describe
motion of the electron.
Moving electrons in stable states (orbits) do not
radiate. It radiates when an electron making a
transition between the orbits.
The orbital angular momenta of the electrons are
quantized.
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2017/5/24
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Chapter 2, Atomic Physics
Quanta in the atom
 The total energy of the electron is inversely
proportional to the square of n, i.e. En   12 where n
n
is called quantum number.
 The total energy is also found to be negative,
indicating a “bound” state. The most negative state,
the most tightly bound electron, occurs for n=1,
referred to as the ground state of the atom, n>=2,
excited states.
 The angular momentum of the electron moving in a
circular orbit can only take discrete values: L  n
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2017/5/24
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Chapter 2, Atomic Physics
Line spectra of the H atom
 Energy levels:
1 2
e2
m  e2  1
 2
En  mv 
  2 
2
40 r
2  40  n
 Lyman series: n=1;
Balmer series: n=2;
Paschen series: n=3;
Brackett series: n=4
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2017/5/24
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Chapter 2, Atomic Physics
Improvement on the Bohr model
 Finite nuclear mass (motion of nucleus): When taking
the nuclear mass into account, the reduced mass
should replace the electron mass.
 Relativistic correction: The effect of the relativistic
mass change m(v) should be considered.
Fastermassivedecrease in energy.
 Sommerfeld’s extension: Electrons should have
elliptical orbits with the same energies as that in
circular orbits. The second quantum number should
be introduced.
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2017/5/24
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Chapter 2, Atomic Physics
Frank-Hertz experiment
 Frank & Hertz in 1913 showed the existence of
discrete energy levels in atoms.
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2017/5/24
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Chapter 2, Atomic Physics
Frank-Hertz experiment results
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2017/5/24
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Chapter 2, Atomic Physics
Explanation
 With the increase of grid potential, more electrons
move to the plate and the current rises accordingly.
 For mercury atoms, when V=4.9V, the electrons
make inelastic collision and leave the atom jump to a
high orbit (n=2). The original electrons move off with
little energy and could not reach the plate and thus
reduce the current.
 As V is increased further, the current rises again and
would drop at V=9.8V. This would make more atoms
to jump to n=2 state.
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2017/5/24
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Chapter 2, Atomic Physics
Limitations of Bohr model
 It can not be generalised to deal with systems with
two more electrons as the force between the
electrons can not be easily added.
 It can not explain the closely spaced lines.
 It can not be used to calculate the rate of
transitions between different energy levels.
 The Bohr model was eventually superseded by the
quantum mechanics developed by E Schrodinger,
W Heisenberg and others, following the ideas of L
de Broglie.
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2017/5/24
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