Chemistry
2302
Atomic
Emission
Winter
2012
The
Atomic
Emission
Spectra
of
Hydrogen,
Deuterium
and
Sodium
Recommended
Preparatory
Reading
• Experiment
30
in
Sime
(2)
entitled
“Visible
Spectrum
of
the
Hydrogen
Atom”
• Experiment
40
in
Shoemaker
(1)
entitled
“Spectrum
of
the
Hydrogen
Atom”
Introduction
If
you
have
completed
the
Vibrational-‐Rotational
Spectrum
of
HCl/DCl
experiment
you
might
have
noticed
that
the
spacing
of
rotational
and
vibrational
energy
levels
is
quite
small,
consequently,
the
electron
transitions
are
observed
in
the
infrared
region
of
the
electromagnetic
spectrum.
In
comparison,
the
spacing
of
electronic
energy
levels
is
quite
large.
To
produce
electronic
transitions
between
energy
levels
in
gaseous
atoms,
the
gas
is
placed
in
a
Geissler
discharge
tube
in
which
it
is
subjected
to
a
very
high
voltage.
The
light
produced
falls
within
the
UV-‐visible
region
of
the
spectrum
and
can
separated
into
its
spectral
components
using
a
diffraction
grating
or
a
prism.
The
hydrogen
atom,
having
only
one
electron,
has
a
very
simple
spectrum.
This
spectrum
was
first
studied
by
Balmer
in
1885.
Spectra
for
other
atoms
are
more
complex
since
they
have
more
electrons.
In
this
experiment,
the
electron
emission
spectra
of
hydrogen,
deuterium
and
sodium
will
be
observed
using
two
handheld
spectroscopes
and
a
UV-‐visible
spectrophotometer.
For
the
hydrogen
atom
and
one-‐electron
ions,
the
Schrödinger
equation
can
be
solved
to
give
the
energies,
𝐸 ,
of
the
quantized
electronic
states
having
principal
quantum
number,
𝑛:
𝜇𝑒 !
𝐸! = ! ! ! with 𝑛 = 1, 2, 3, …
8ℎ 𝜀! 𝑛
Equation
1
Here
𝑒
is
the
charge
on
an
electron,
h
is
Planck’s
constant,
and
ε0
is
the
permittivity
of
vacuum.
𝜇 ,
the
reduced
mass,
in
this
case
is
given
by:
𝑚! 𝑚!
𝜇 =
𝑚! + 𝑚!
Equation
2
where
𝑚!
is
the
mass
of
an
electron
and
𝑚!
is
the
mass
of
a
proton.
In
your
report,
simply
give
the
relationship,
carefully
defining
all
terms
and
presenting
any
assumptions
that
allow
application
of
this
particular
relationship
to
your
systems.
When
an
electron
in
an
atom
changes
from
a
higher
energy
state,
E1,
to
one
of
lower
energy,
E2,
a
photon
is
emitted.
The
change
in
energy
is:
𝐸! − 𝐸! = ℎ𝑐𝜈
Equation
3
Chemistry
2302
Atomic
Emission
Winter
2012
where
𝑐
is
the
speed
of
light
and
𝜈
is
the
energy
of
the
photon
in
wavenumbers
(cm-‐1).
When
equations
1
and
3
are
combined,
the
following
equation
is
obtained
allowing
the
calculation
of
the
energy
of
the
emitted
photon:
1 1
𝜈 = 𝑅 ! − !
𝑛! 𝑛!
Equation
4
!!! !! !
where
𝑅
is
the
Rydberg
constant
given
by
𝑅 = .
It
equals
109677.8
cm-‐1
for
!.!!!"#×!"!!" !! !!! !! ! !! !
the
hydrogen
atom.
𝑛!
is
the
principal
quantum
number
of
the
lower
energy
state
and
𝑛!
that
of
the
higher
energy
state.
The
theoretical
wavelength
of
the
photon
may
be
easily
obtained
by
calculating
the
reciprocal
of
𝜈 .
Sime’s
(2)
figure
30-‐1
shows
some
of
the
electron
transitions
that
can
occur
for
the
hydrogen
atom.
This
experiment
will
concentrate
on
the
ones
that
terminate
at
the
𝑛! = 2
energy
level,
called
the
Balmer
series.
The
energy
of
four
lines
in
the
Balmer
series,
the
isotopic
separation
of
hydrogen/deuterium
emission
lines,
and
the
spacing
of
sodium
doublets
will
be
determined.
Explain
how
attributing
an
intrinsic
(spin)
angular
momentum,
S,
to
the
electron
in
addition
to
the
orbital
component,
L,
produces
a
total
angular
momentum,
J,
which
can
account
for
the
fine
structure
(doublets)
present
in
the
sodium
atomic
emission
spectrum.
Section
13.2
of
your
textbook
(Laidler)
will
help
you
with
this
explanation.
A
Russell-‐Saunders
term
symbol
can
be
written
for
each
electronic
energy
level
of
an
atom.
It
has
the
form
n(2S
+1)LJ
where
n
is
the
principle
quantum
number.
Define
the
other
elements
(S,
2S+1,
L
and
J)
of
the
term
symbol
and
explain
how
values
for
each
are
assigned.
Again
Section
13.2
of
your
textbook
will
be
of
assistance
to
you.
Also,
section
13.9
of
Physical
Chemistry
by
Atkins
&
de
Paula
is
quite
good
and
available
in
C-‐3041.
Experimental
Preliminary
Observations:
Observe,
using
the
handheld
spectroscope,
the
emission
from
a
hydrogen
discharge
tube.
Sketch
the
emission
spectra,
indicating
the
color
and
approximate
wavelengths
of
the
4
strongest
lines.
Now
observe
using
a
Bleeker
prism
spectroscope
and
again
note
the
wavelengths
of
the
same
four
lines.
Note
the
precision
of
each
spectroscope.
Also
available
for
observation
are
neon,
argon,
and
chlorine
discharge
tubes,
and,
of
course,
overhead
lights,
sunlight,
etc.
for
the
curious.
Follow
instructions
provided
in
the
lab
carefully.
The
power
supply
operates
at
a
high
voltage...use
care!
Measurement:
Measure
the
spectra
in
the
visible
region
of
hydrogen,
deuterium
and
sodium
using
the
Ocean
Optics
S2000
fibre
optic
spectrometer.
Note
its
precision.
This
small
grating
spectrometer
comprises
miniaturized
optical
components,
a
CCD
detector,
and
accesses
light
via
a
fibre
optic
cable!
To
perform
a
measurement,
open
the
OOIBase32
software
used
to
control
the
spectrophotometer.
Point
the
fibre
optic
cable
toward
the
middle
of
the
discharge
tube.
The
spectrum
is
constantly
updated
Chemistry
2302
Atomic
Emission
Winter
2012
on
the
screen
in
real
time.
You
may
need
to
move
the
fibre
optic
cable
around
slightly
until
the
intensities
of
the
peaks
are
reasonable
(i.e.
you
should
be
able
to
see
the
4
peaks
but
the
highest
one
must
not
go
off
scale).
Once
the
intensities
are
to
your
liking,
hold
the
cable
very
still
and
click
the
camera
button.
This
will
freeze
the
spectrum.
If
your
hand
is
unsteady
you
may
choose
to
mount
the
fibre
optic
cable
in
a
clamp
attached
to
a
ring
stand.
Save
each
spectrum
by
clicking
on
File
à
Save
As
à
Sample.
Repeat
for
the
deuterium
discharge
tube
and
the
large
(bright!)
sodium
source
lamp.
Before
leaving,
transfer
the
saved
data
files
to
a
flash
drive
(or
e-‐mail
them
to
yourself)
as
you
will
need
them
to
complete
the
lab
report.
The
files
contain
two
columns
of
data
–
a
column
of
wavelengths
(nm)
and
a
column
of
intensity
values.
Results
The
spectra
that
you
saved
during
the
experiment
will
have
the
extension
.wav.
Open
these
files
in
Notepad
(or
other
simple
text
editing
software).
Copy
the
columns
of
data
(wavelengths
and
intensities)
and
paste
them
into
a
spreadsheet.
For
all
species,
recreate
the
spectrum
you
observed
during
the
experiment
by
plotting
a
graph
of
intensity
versus
wavelength.
Choose
a
graph
type
that
will
draw
a
smooth
line
through
the
data
points
without
displaying
the
actual
points.
Enlarge
(zoom
in
on)
the
four
strongest
emission
lines
in
only
the
hydrogen
spectrum
and
submit
these
as
individual
plots.
Identify
the
upper
and
lower
states
of
each
strong
spectral
line
measured
by
its
atomic
term
symbol
n(2S
+
1)LJ
.
You
will
need
to
consult
the
literature
for
these
assignments.
An
energy
level
diagram
for
hydrogen
can
be
found
in
Sime.
The
diagram
for
sodium
(taken
from
Noggle)
is
given
later
in
this
outline.
On
your
printed
spectra,
next
to
each
intense
peak,
identify
the
electronic
transition
responsible
for
its
presence
with
the
term
symbols.
The
notation
representing
an
electron
transition
is
written
follows:
Upper
state
term
symbol
à
Lower
state
term
symbol
For
hydrogen
and
deuterium,
only
consider
the
4
strongest
emission
peaks.
For
sodium
you
need
only
consider
the
first
line
in
the
principle
series
(see
the
diagrams
on
the
next
two
pages,
from
Noggle).
Hydrogen
Correct
the
wavelengths
observed
in
air,
of
the
hydrogen
emission
lines,
to
vacuum
then
convert
the
wavelengths
to
wavenumbers
(cm-‐1).
The
correction
involves
the
refractive
index
of
air
and
can
be
found
in
Shoemaker.
Now
use
equation
4
to
calculate
the
four
theoretical
energies
of
the
emitted
photons
for
the
first
four
lines
in
the
Balmer
series.
Deuterium
As
for
hydrogen,
correct
the
observed
wavelengths
of
the
four
emission
lines
to
vacuum
then
convert
to
wavenumbers.
Calculate
the
Rydberg
constant
for
deuterium
(Hint:
what
is
added
to
a
hydrogen
atom
to
make
deuterium?)
and
use
equation
4
to
calculate
the
theoretical
energies
of
the
emitted
photons
for
the
four
lines.
Chemistry
2302
Atomic
Emission
Winter
2012
As
you
have
probably
noticed,
the
spectrum
for
hydrogen
and
deuterium
are
almost
the
same,
except
that
each
line
is
shifted
to
a
slightly
higher
energy
in
the
deuterium
spectrum.
Using
your
calculated
theoretical
wavenumbers,
calculate
the
isotopic
shift
(difference
in
energy)
for
each
corresponding
pair
of
lines.
Organize
the
data
for
hydrogen
and
deuterium
into
a
table
with
the
following
four
headings:
Isotope,
Transition
(term
symbol
notation),
𝜈!"# ,
𝜈!!!"#$
Sodium
Write
term
symbols
denoting
electron
transitions
for
the
first
four
lines
in
the
principal
series
(see
the
term
diagram
below).
Note
that
each
line
in
this
series
is
a
doublet
(called
the
“fine
structure”),
although
the
fibre
optic
spectrometer
that
we
used
does
not
have
a
high
enough
resolution
to
see
them.
Print
your
spectrum
and
try
to
find
peaks
corresponding
the
principal
series
transitions
(see
the
diagram
below
for
wavelengths
of
the
first
five
lines
in
the
principle
series).
If
you
can
find
the
peaks,
label
them
with
the
term
symbols
you
have
written.
Measure
the
separation
of
the
doublet
for
the
first
lines
in
the
principal
and
sharp
series.
Since
you
cannot
see
the
doublets
on
your
experimental
spectrum
you
must
use
the
spectra
provided
on
the
page
after
next,
which
were
measured
on
the
Coderg
Raman
spectrometer
with
a
precision
of
~
1
cm-‐1.
The
spectrum
on
the
top
is
for
the
first
line
in
the
sharp
series
and
on
the
bottom
is
for
the
first
line
in
the
principal
series.
Chemistry
2302
Atomic
Emission
Winter
2012
Chemistry
2302
Atomic
Emission
Winter
2012
Chemistry
2302
Atomic
Emission
Winter
2012
Discussion
Contrast
the
construction,
optics,
range,
resolution,
sensitivity,
method
of
detection,
and
applicability
of
the
two
relatively
simple
spectroscopes
and
fibre
optic
spectrometer.
A
cracked-‐open
spectroscope
is
on
display.
Compare
your
experimental
energies
of
the
strong
emission
lines
of
hydrogen,
deuterium
and
sodium
with
the
literature
values.
Remember,
you
have
already
calculated
the
“literature”
values
for
hydrogen
and
deuterium
in
the
results
section.
The
literature
values
for
the
sodium
principal
series
lines
are
given
in
the
diagram
on
page
3.
Hydrogen
and
Deuterium
Compare
the
experimental
isotopic
shift
with
the
theoretical
isotopic
shift.
Address
the
applicability
to
your
systems,
any
assumptions
made
in
the
development
of
the
theory.
If
the
hydrogen
and
deuterium
emission
spectra
had
been
measured
simultaneously,
instead
of
individually,
would
the
isotopic
separation
have
been
observed?
What
resolution
would
be
required
to
see
the
isotopic
shift
of
a
hydrogen
/
deuterium
mixture?
Sodium
Compare
the
experimental
splitting
observed
in
each
doublet
with
the
splitting
reported
in
the
literature
(see
the
term
diagram
on
page
3
for
literature
values
for
the
first
line
in
the
principle
series)
References
Available
in
the
lab:
1.
Shoemaker
et
al.,
"Experiments
in
Physical
Chemistry",
5th
ed.,
McGraw
Hill,
Toronto
(1962).
2.
Rodney
J.
Sime,
"Physical
Chemistry",
Holt,
Rinehart,
and
Winston.
Orlando,
1990.
3.
Frank
L.
Pilar.
Elementary
Quantum
Chemistry.
McGraw-‐Hill
Publishing
Company,
Toronto.
1990.
4.
Ira
N.
Levine,
Quantum
Mechanics,
5th
Edition,
Prentice
Hall,
New
Jersey,
2000.
Available
on
reserve
in
library:
5.
G.
Herzberg,
"Atomic
Spectra
and
Atomic
Structure",
Dover
Publications,
New
York
(1944).
6.
H.G.
Kuhn,
"Atomic
Spectra".
Available
in
lab
and
in
periodicals
section
of
library:
7.
Fred
Stafford
and
James
H.
Wortman,
J.Chem.
Ed.
39
(1962),
630.
