Transcript Welcome to PHY 1371

Chapter 42
Atomic Physics
Dr. Jie Zou
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Outline
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Atomic spectra of gases
Early models of the atom
Bohr’s model of the hydrogen atom
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Atomic spectra of gases
Orion Nebula
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(a) Emission line spectra for H, Hg, and Ne.
(b) Absorption spectrum for H.
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“Neon” signs: an application
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Balmer series of hydrogen
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Johann Jocob Balmer (18251898)
The empirical equation by
Johannes Rydberg (1854-1919):
1 
 1
 RH  2  2  n  3,4,5,...
RH: Rydberg
n 
 2 constant
= 1.0973732
1
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The Balmer series of spectral lines
for atomic hydrogen.
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x 107 m-1.
The series limit
The measured spectral lines agree
with the empirical equation to
within 0.1%.
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Early models of the atom
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Model of the atom in the
days of Newton: Tiny,
hard, and indestructible
sphere.
J.J. Thomson’s model of
the atom: Negatively
charged electrons in a
volume of continuous
positive charge.
Rutherford’s planetary
model of the atom.
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Difficulties with Rutherford’s
planetary model
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Cannot explain the
phenomenon that an atom
emits (and absorbs) certain
characteristic frequencies of
electromagnetic radiation and
no others.
Predication of the ultimate
collapse of the atom as the
electron plunges into the
nucleus.
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Bohr’s model of the hydrogen
atom
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Basic ideas of the Bohr theory of the hydrogen atom:
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The electron moves in circular orbits around the proton
under the electric force of attraction.
Only certain electron orbits are stable. When in one of these
stationary states, the electron does not emit energy in
the form of radiation.
Radiation is emitted by the atom when the electron makes a
transition from a more energetic initial orbit to a lowerenergy orbit. The frequency of the emitted radiation is
found from Ei –Ef = hf. Energy of an incident photon can be
absorbed by the atom only if the photon has an energy that
exactly matches the difference in energy between an
allowed state of the atom and its existing state upon
incidence of the photon.
The size of an allowed electron orbit is determined by a
condition imposed on the electron’s orbital angular
momentum: quantization of the orbital angular momentum
mevr=nħ, n = 1,2,3…
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Bohr’s theory of hydrogen
atom (cont.)
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Allowed energy levels (see detailed derivation):
ke e 2  1 
13.606
En  
eV
n  1,2,3,...
 2
2
2a0  n 
n
a0 = Bohr radius = ħ2/mekee2 = 0.0529 nm
2
2
 rn =n a0 = n (0.0529 nm)
 Ionization energy: the minimum energy required to
ionize the atom in its ground state (to completely remove
an electron from the proton’s influence) = 13.6 eV for
hydrogen.
Ei  E f
ke e 2  1
1 
f 

 2
2

h
2a0 h  n f ni 
Emission frequency and wavelength:
k e e 2  1
1 f
1 
 
 2
2

 c 2a0 hc  n f ni 
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Energy-level diagram for the
hydrogen atom
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Quick quiz #1
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A hydrogen atom is in its ground state.
Incident on the atom are many photons
each having an energy of 10.5 eV. The
result is that
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(a) the atom is excited to a higher allowed
state
(b) the atom is ionized
(c) the photons pass by the atom without
interaction
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Quick Quiz #2
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A hydrogen atom makes a transition from the
n = 3 level to the n = 2 level. It then makes a
transition from the n = 2 level to the n = 1
level. Which transition results in emission of
the longest-wavelength photon?
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(a) the first transition
(b) the second transition
(c) neither, because the wavelengths are the same
for both transitions.
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Homework
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Chapter 42, P. 1392, Problems: #5, 6,
8, 12.
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