Atomic Spectroscopy and NucleaSimplest Atomic Spectrum: Hydrogenr

PY3P05
Lecture 1-2: Introduction to Atomic Spectroscopy
Lecture 1-2: Introduction to Atomic Spectroscopy
o Line spectra
o Emission spectra
o Absorption spectra
o Hydrogen spectrum
o Balmer Formula
o Bohr’s Model
Bulb
Sun
Na
H
Hg
Cs
Chlorophyll
Diethylthiacarbocyaniodid
Diethylthiadicarbocyaniodid
Absorption
spectra
Emission
spectra

PY3P05
Types of Spectra
Types of Spectra
o Continuous spectrum: Produced by solids, liquids & dense gases produce - no
“gaps” in wavelength of light produced:
o Emission spectrum: Produced by rarefied gases – emission only in narrow
wavelength regions:
o Absorption spectrum: Gas atoms absorb the same wavelengths as they
usually emit and results in an absorption line spectrum:

PY3P05
Emission and Absorption Spectroscopy
Emission and Absorption Spectroscopy
Gas cloud
1
2
3

PY3P05
Line Spectra
Line Spectra
o Electron transition between energy levels result in emission or absorption lines.
o Different elements produce different spectra due to differing atomic structure.
H
He
C
 

PY3P05
Emission/Absorption of Radiation by Atoms
o Emission/absorption lines are due to radiative transitions:
1. Radiative (or Stimulated) absorption:
Photon with energy (E = h = E2 - E1) excites electron from lower energy
level.
Can only occur if E = h = E2 - E1
2. Radiative recombination/emission:
Electron makes transition to lower energy level and emits photon with energy
h’
= E2 - E1.
E2
E1
E2
E1
E =h

PY3P05
o Radiative recombination can be either:
a) Spontaneous emission: Electron minimizes its total energy by emitting photon and making
transition from E2 to E1.
Emitted photon has energy E
’
= h’
= E2 - E1
b) Stimulated emission: If photon is strongly coupled with electron, cause electron to decay to
lower energy level, releasing a photon of the same energy.
Can only occur if E = h = E2 - E1 Also, h’
= h
E2
E1
E2
E1
E2
E1
E2
E1
E
’
=h’
E =h
E
’
=h’
E =h

PY3P05
Simplest Atomic Spectrum: Hydrogen
o In ~1850’s, optical spectrum of hydrogen was found to contain strong lines at 6563,
4861 and 4340 Å.
o Lines found to fall closer and closer as wavelength decreases.
o Line separation converges at a particular wavelength, called the series limit.
o Balmer found that the wavelength of lines could be written
where n is an integer >2, and RH is the Rydberg constant.
6563 4861 4340
H H H
 (Å)

PY3P05
o If n =3, =>
o Called H - first line of Balmer series.
o Other lines in Balmer series:
o Balmer Series limit occurs when n .
Å
Highway 6563 in New
Mexico
Å
Name Transitions Wavelength (Å)
H
3 - 2 6562.8
H
4 - 2 4861.3
H
5 - 2 4340.5

PY3P05
Lyman UV nf = 1, ni2
Balmer Visible/UV nf = 2, ni3
Paschen IR nf = 3, ni4
Brackett IR nf = 4, ni5
Pfund IR nf = 5, ni6
Series Limits
o Other series of hydrogen:
o Rydberg showed that all series above could be
reproduced using
o Series limit occurs when ni = ∞, nf = 1, 2, …

PY3P05
o Term or Grotrian diagram for
hydrogen.
o Spectral lines can be considered as
transition between terms.
o A consequence of atomic energy levels,
is that transitions can only occur
between certain terms. Called a
selection rule. Selection rule for
hydrogen: n = 1, 2, 3, …

PY3P05
Bohr Model for Hydrogen
o Simplest atomic system, consisting of single electron-proton pair.
o First model put forward by Bohr in 1913. He postulated that:
1. Electron moves in circular orbit about proton under Coulomb attraction.
2. Only possible for electron to orbits for which angular momentum is quantised,
ie., n = 1, 2, 3, …
3. Total energy (KE + V) of electron in orbit remains constant.
4. Quantized radiation is emitted/absorbed if an electron moves changes its
orbit.

PY3P05
o Consider atom consisting of a nucleus of charge +Ze and mass M, and an electron on
charge -e and mass m. Assume M>>m so nucleus remains at fixed position in space.
o As Coulomb force is a centripetal, can write (1)
o As angular momentum is quantised (2nd postulate): n = 1, 2, 3, …
o Solving for v and substituting into Eqn. 1 => (2)
o The total mechanical energy is:
o Therefore, quantization of AM leads to quantisation of total energy.
n = 1, 2, 3, … (3)

PY3P05
o Substituting in for constants, Eqn. 3 can be written eV
and Eqn. 2 can be written where a0 = 0.529 Å = “Bohr radius”.
o Eqn. 3 gives a theoretical energy level structure for hydrogen (Z=1):
o For Z = 1 and n = 1, the ground state of hydrogen is: E1 = -13.6 eV

PY3P05
o The wavelength of radiation emitted when an electron makes a transition, is (from
4th postulate):
or (4)
where
o Theoretical derivation of Rydberg formula.
o Essential predictions of Bohr model
are contained in Eqns. 3 and 4.

PY3P05
Correction for Motion of the Nucleus
o Spectroscopically measured RH does not agree exactly with theoretically derived
R∞.
o But, we assumed that M>>m => nucleus fixed. In reality, electron and proton
move about common centre of mass. Must use electron’s reduced mass ():
o As m only appears in R∞, must replace by:
o It is found spectroscopically that RM = RH to within three parts in 100,000.
o Therefore, different isotopes of same element have slightly different spectral lines.

PY3P05
o Consider 1
H (hydrogen) and 2
H (deuterium):
o Using Eqn. 4, the wavelength difference is
therefore:
o Called an isotope shift.
o H and D are separated by about 1Å.
o Intensity of D line is proportional to fraction of D
in the sample.
cm-1
cm-1
Balmer line of H and D

PY3P05
Spectra of Hydrogen-like Atoms
o Bohr model works well for H and H-like atoms (e.g., 4
He+
, 7
Li2+
, 7
Be3+
, etc).
o Spectrum of 4
He+
is almost identical to H, but just offset by a factor of four (Z2
).
o For He+
, Fowler found the following
in stellar spectra:
o See Fig. 8.7 in Haken & Wolf.
0
20
40
60
80
100
120
Energy
(eV)
1
n
2
1
2
3
Z=1
H
Z=2
He+
Z=3
Li2+
n n
1
2
3
4
13.6 eV
54.4 eV
122.5 eV

PY3P05
o Hydrogenic or hydrogen-like ions:
o He+
(Z=2)
o Li2+
(Z=3)
o Be3+
(Z=4)
o …
o From Bohr model, the ionization energy is:
E1 = -13.59 Z2
eV
o Ionization potential therefore increases rapidly with Z.
Hydrogenic
isoelectronic
sequences
0
20
40
60
80
100
120
Energy
(eV)
1
n
2
1
2
3
Z=1
H
Z=2
He+
Z=3
Li2+
n n
1
2
3
4
13.6 eV
54.4 eV
122.5 eV

PY3P05
Implications of Bohr Model
Implications of Bohr Model
o We also find that the orbital radius and velocity are quantised:
and
o Bohr radius (a0) and fine structure constant () are fundamental constants:
and
o Constants are related by
o With Rydberg constant, define gross atomic characteristics of the atom.
Rydberg energy RH 13.6 eV
Bohr radius a0 5.26x10-11
m
Fine structure constant  1/137.04

PY3P05
Exotic Atoms
Exotic Atoms
o Positronium
o electron (e-
) and positron (e+
) enter a short-lived bound state, before they
annihilate each other with the emission of two -rays (discovered in 1949).
o Parapositronium (S=0) has a lifetime of ~1.25 x 10-10
s. Orthopositronium (S=1)
has lifetime of ~1.4 x 10-7
s.
o Energy levels proportional to reduced mass => energy levels half of hydrogen.
o Muonium:
o Replace proton in H atom with a  meson (a “muon”).
o Bound state has a lifetime of ~2.2 x 10-6
s.
o According to Bohr’s theory (Eqn. 3), the binding energy is 13.5 eV.
o From Eqn. 4, n = 1 to n = 2 transition produces a photon of 10.15 eV.
o Antihydrogen:
o Consists of a positron bound to an antiproton - first observed in 1996 at CERN!
o Antimatter should behave like ordinary matter according to QM.
o Have not been investigated spectroscopically … yet.

PY3P05
Failures of Bohr Model
o Bohr model was a major step toward understanding the quantum theory of the atom
- not in fact a correct description of the nature of electron orbits.
o Some of the shortcomings of the model are:
1. Fails describe why certain spectral lines are brighter than others => no
mechanism for calculating transition probabilities.
2. Violates the uncertainty principal which dictates that position and momentum
cannot be simultaneously determined.
o Bohr model gives a basic conceptual model of electrons orbits and energies. The
precise details can only be solved using the Schrödinger equation.

PY3P05
o From the Bohr model, the linear momentum of the electron is
o However, know from Hiesenberg Uncertainty Principle, that
o Comparing the two Eqns. above => p ~ np
o This shows that the magnitude of p is undefined except when n is large.
o Bohr model only valid when we approach the classical limit at large n.
o Must therefore use full quantum mechanical treatment to model electron in H atom.

PY3P05
Hydrogen Spectrum
Hydrogen Spectrum
o Transitions actually depend on more than a
single quantum number (i.e., more than n).
o Quantum mechanics leads to introduction on
four quntum numbers.
o Principal quantum number: n
o Azimuthal quantum number: l
o Magnetic quantum number: ml
o Spin quantum number: s
o Selection rules must also be modified.

PY3P05
Atomic Energy Scales
Atomic Energy Scales
Energy scale Energy (eV) Effects
Gross structure 1-10 electron-nuclear
attraction
Electron kinetic energy
Electron-electron
repulsion
Fine structure 0.001 - 0.01 Spin-orbit interaction
Relativistic corrections
Hyperfine structure 10-6
- 10-5
Nuclear interactions

Atomic Spectroscopy and NucleaSimplest Atomic Spectrum: Hydrogenr

More Related Content

Similar to Atomic Spectroscopy and NucleaSimplest Atomic Spectrum: Hydrogenr (20)

Recently uploaded (20)

Atomic Spectroscopy and NucleaSimplest Atomic Spectrum: Hydrogenr