Copyright © 2015, W. W. Norton & Company
Prepared by Dr. Mai Khaleel,
Isra University
Lecture Slides
CHAPTER 1: Electrons, photons, and atoms
Physics of Atoms and Molecules
B. H. Bransden (Author), Charles J.
05/04/2021
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These lecture slides cover the topic of atomic models and the hydrogen spectrum in the context of Physics of Atoms and Molecules. various atomic models, including Balmer, Rydberg, and Bohr models, and their predictions for the wavelengths of photons emitted during electron transitions. The slides also touch upon the limitations of the Bohr model and the Franck-Hertz experiment that demonstrated the concept of quantization of energy levels.
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Copyright © 2015 , W. W. Norton & Company
Prepared by Dr. Mai Khaleel,
Isra University
Lecture Slides
CHAPTER 1 : Electrons, photons, and atoms
Physics of Atoms and Molecules
B. H. Bransden (Author), Charles J.
05 / 04 / 2021
▪ Balmer : gave an empirical formula for hydrogen spectrum.
used to determine the wavelengths of the four visible lines of the hydrogen line spectrum
Lyman series with n 1 = 1
Balmer series with n 1 = 2
Paschen series with n 1 = 3
Rydberg Formula
Derivative of the Balmer formula.
Predicts the wavelength of photons that are emitted when
an electron moves back to the ground state from its
excited state.
R = 10973731.57 m− 1
1
𝜆
= 𝑅 𝑍
2 (
1
𝑛 1
2
−
1
𝑛 2
2
)
Hydrogen atom
1
𝜆
= 𝑅 (
1
𝑛 1
2
−
1
𝑛 2
2
)
1
frequency
wavenumber
R = 1097373 m− 1
For one electron atom:
Limitations of Bohr model
▪ In Bohr's equation, the momentum and position of electron, revolving around the nucleus were well
defined. But, according, Heisenberg's Uncertainty principle, it is impossible to measure the position
and momentum of electrons precisely. If the position is measure with maximum precision, there will
be uncertainty in the value of momentum and vice versa.
Franck-Hertz Experiment
▪ Aim: To experimentally demonstrate the concept of quantization of energy levels according to
Bohr’s model of atom.
▪ Apparatus: A mercury-filled Franck-Hertz tube, a control unit for power supply, and a DC current
amplifier.
▪ Sketch of Franck-Hertz Apparatus
Finite nuclear mass
Finite nuclear mass
infinite nuclear mass
Finite nuclear mass
System in equilibrium, using center of mass theory
Finite nuclear mass correction
The allowed values of r:
Rydberg constant of the nucleus of mass M interns of R(∞) and
Copyright © 2015 , W. W. Norton & Company
Prepared by Dr. Mai Khaleel,
Isra University
CHAPTER 1 : Electrons,
photons, and atoms
This concludes the Lecture slides for
Physics of Atoms and Molecules
B. H. Bransden (Author), Charles J.