PHY206: Atomic Spectra

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PHY206 Atomic Spectra

• Lecturer Dr Stathes Paganis
• Office D29, Hicks Building
• Phone [phone]
• Email paganis_at_NOSPAMmail.cern.ch
• Text A. C. Phillips, Introduction to QM
• http//www.shef.ac.uk/physics/teaching/phy206
• Marks Final 70, Homework 2x10, Problems Class
  10

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Course Outline (1)

• Lecture 1 Bohr Theory
• Introduction
• Bohr Theory (the first QM picture of the atom)
• Quantum Mechanics
• Lecture 2 Angular Momentum (1)
• Orbital Angular Momentum (1)
• Magnetic Moments
• Lecture 3 Angular Momentum (2)
• Stern-Gerlach experiment the Spin
• Examples
• Orbital Angular Momentum (2)
• Operators of orbital angular momentum
• Lecture 4 Angular Momentum (3)
• Orbital Angular Momentum (3)
• Angular Shapes of particle Wavefunctions
• Spherical Harmonics
• Examples

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Course Outline (2)

• Lecture 5 The Hydrogen Atom (1)
• Central Potentials
• Classical and QM central potentials
• QM of the Hydrogen Atom (1)
• The Schrodinger Equation for the Coulomb
  Potential
• Lecture 6 The Hydrogen Atom (2)
• QM of the Hydrogen Atom (2)
• Energy levels and Eigenfunctions
• Sizes and Shapes of the H-atom Quantum States
• Lecture 7 The Hydrogen Atom (3)
• The Reduced Mass Effect
• Relativistic Effects

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Course Outline (3)

• Lecture 8 Identical Particles (1)
• Particle Exchange Symmetry and its Physical
  Consequences
• Lecture 9 Identical Particles (2)
• Exchange Symmetry with Spin
• Bosons and Fermions
• Lecture 10 Atomic Spectra (1)
• Atomic Quantum States
• Central Field Approximation and Corrections
• Lecture 11 Atomic Spectra (2)
• The Periodic Table
• Lecture 12 Review Lecture

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Atoms, Protons, Quarks and Gluons
Atomic Nucleus
Atom
Proton
Proton
gluons
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Atomic Structure
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Early Models of the Atom

• Rutherfords model
• Planetary model
• Based on results of thin foil experiments (1907)
• Positive charge is concentrated in the center of
  the atom, called the nucleus
• Electrons orbit the nucleus like planets orbit
  the sun

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atoms should collapse
Classical Physics
Classical Electrodynamics charged particles
radiate EM energy (photons) when their velocity
vector changes (e.g. they accelerate).
This means an electron should fall into the
nucleus.
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Light the big puzzle in the 1800s
Light from the sun or a light bulb has a
continuous frequency spectrum
Light from Hydrogen gas has a discrete frequency
spectrum
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Emission lines of some elements (all quantized!)
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Emission spectrum of Hydrogen

• Quantized spectrum

• Continuous spectrum

DE
DE
Any DE is possible
Only certain DE are allowed

• Relaxation from one energy level to another by
  emitting a photon, with DE hc/l
• If l 440 nm, DE 4.5 x 10-19 J

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Emission spectrum of Hydrogen
The goal use the emission spectrum to determine
the energy levels for the hydrogen atom
(H-atomic spectrum)
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Balmer model (1885)

• Joseph Balmer (1885) first noticed that the
  frequency of visible lines in the H atom spectrum
  could be reproduced by

n 3, 4, 5, ..

• The above equation predicts that as n increases,
  the frequencies become more closely spaced.

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Rydberg Model

• Johann Rydberg extended the Balmer model by
  finding more emission lines outside the visible
  region of the spectrum

n1 1, 2, 3, ..
n2 n11, n12,
Ry 3.29 x 1015 1/s

• In this model the energy levels of the H atom are
  proportional to 1/n2

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The Bohr Model (1)

• Bohrs Postulates (1913)
• Bohr set down postulates to account for (1) the
  stability of the hydrogen atom and (2) the line
  spectrum of the atom.

• Energy level postulate An electron can have only
  specific energy levels in an atom.
• Electrons move in orbits restricted by the
  requirement that the angular momentum be an
  integral multiple of h/2p, which means that for
  circular orbits of radius r the z component of
  the angular momentum L is quantized
• 2. Transitions between energy levels An electron
  in an atom can change energy levels by undergoing
  a transition from one energy level to another.

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The Bohr Model (2)

• Bohr derived the following formula for the energy
  levels of the electron in the hydrogen atom.
• Bohr model for the H atom is capable of
  reproducing the energy levels given by the
  empirical formulas of Balmer and Rydberg.

Energy in Joules Z atomic number (1 for H) n is
an integer (1, 2, .)
The Bohr constant is the same as the Rydberg
multiplied by Plancks constant!
Ry x h -2.178 x 10-18 J
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The Bohr Model (3)
Energy levels get closer together as n
increases
at n infinity, E 0
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Prediction of energy spectra
We can use the Bohr model to predict what DE
is for any two energy levels
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Example calculation (1)
Example At what wavelength will an emission
from n 4 to n 1 for the H atom be
observed?
1
4
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Example calculation (2)
Example What is the longest wavelength of
light that will result in removal of the e- from
H?
?
1
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Bohr model extedned to higher Z
The Bohr model can be extended to any single
electron system.must keep track of Z (atomic
number).
Z atomic number
n integer (1, 2, .)
Examples He (Z 2), Li2 (Z 3), etc.
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Example calculation (3)
Example At what wavelength will emission
from n 4 to n 1 for the He atom be
observed?
2
1
4
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Problems with the Bohr model

• Why electrons do not collapse to the nucleus?
• How is it possible to have only certain fixed
  orbits available for the electrons?
• Where is the wave-like nature of the electrons?

First clue towards the correct theory De Broglie
relation (1923)
Einstein
De Broglie relation particles with certain
momentum, oscillate with frequency hv.
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Quantum Mechanics

• Particles in quantum mechanics are expressed by
  wavefunctions
• Wavefunctions are defined in spacetime (x,t)
• They could extend to infinity (electrons)
• They could occupy a region in space
  (quarks/gluons inside proton)
• In QM we are talking about the probability to
  find a particle inside a volume at (x,t)
• So the wavefunction modulus is a Probability
  Density (probablity per unit volume)
• In QM, quantities (like Energy) become
  eigenvalues of operators acting on the
  wavefunctions

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QM we can only talk about the probability to
find the electron around the atom there is no
orbit!