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2.6 Spectroscopy
and the hydrogen spectrum
(a) The interaction of electromagnetic
radiation and matter
- Spectroscopy is the study of
how electromagnetic radiation (e.g. light) interacts with matter.
- Studying the spectrum of hydrogen is good
example to start with in studying spectroscopy, which in most cases, is the
interaction of electromagnetic radiation with atoms or molecules at the
quantum level.
- Electromagnetic radiation forms
a wide ranging spectrum from radio - microwave - infrared -
visible light - uv - x-rays - gamma rays.
- Light can be considered as energy
packets (quanta) called photons which have both the properties of a 'particle'
or a transverse 'wave'.
- The relationship between the speed of
light, wavelength of the radiation and the frequency of the photon is given
by ...
-
c =
λ
 ,
λ =
wavelength (m),
= frequency (Hz = s-1),
c = speed of light 3 x 108 ms-1
- The relationship between the energy of the
photon and its wave frequency is given by Planck's Equation
-
E
=
h
where E = energy
of a single photon (J), h = Planck's
Constant (6.63 x 10-34 JHz-1),
= frequency
(Hz)
-
The energy E, is for one photon interacting with one electron in one atom, so
E represents the difference in energy between the two electronic quantum
levels involved.
-
Therefore you need to multiply E by the Avogadro
Constant (NA = 6.02 x 1023 mol-1) to get J mol-1,
and then divide by 1000 to get kJ mol-1
- When atoms absorb energy e.g.
in hot flames, high voltage discharge etc., they can become
excited from their normal stable ground state (n=1 in the case of
hydrogen), up to a higher 'energy level' state.
- When the excited atoms lose energy and
return to the ground state, in doing so they emit electromagnetic radiation, usually
in the infrared, visible or ultraviolet regions.
- The emitted light can be split and
analysed into its constituent frequencies, using a prism or
grating in a spectrometer, to produce an atomic
emission spectrum of 'lines' of different colour.
- Its also possible for the reverse process
to happen, so if light is passed through the atoms in their ground state,
absorption of energy occurs at exactly the same frequencies as observed in
the emission spectrum. This shows up as black lines against the coloured
spectrum background and is known as the absorption spectrum.
- Both emission and absorption spectra
can be used to identify elements from
their 'finger print' pattern, and from the intensity of the 'signal' quantitative
measurements can be made See bottom of page).
- See
Introduction
to Spectroscopy for examples of calculations using the two
equations above and section on this page 2.8
Emission and absorption spectra of elements - the result of electronic
energy level changes
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2.6
(b) The Bohr theory of the hydrogen atom, its
electronic spectrum and calculation of ionisation energy from spectral
data
 Fig 1.
-
To fully appreciate Fig 1. you need to co-study it with
the electronic energy level Fig.2a
below.
-
The hydrogen
spectrum consists of several series of sharp spectral lines and
the 1st series is illustrated in Fig.1
-
Fig. 2a below: The origin of the
series of lines in the hydrogen spectrum.
-
Within each
series, the lines get closer and closer together and eventually
converge.
 Fig 2a.
- The horizontal lines on the
diagram Fig.2a represent the
increasingly higher electronic energy levels, as you go up from the
ground state (closest to the nucleus, shell 1, level 1, principal quantum
number n = 1), to the point where the electron is lost in ionisation
(n = infinity)
- Each series arises from the possible
electronic transitions between a particular level and all the levels
above it e.g.
- The 1st or Lyman Series, arise from
electronic transitions between n = 1
(ground state of H) and n = 2, 3, 4 etc. (ultra-violet region).
- The 2nd or Balmer Series,
arise from electronic transitions between
n = 2 and n = 3, 4, 5, etc. (visible - infrared regions).
- The 3rd or Paschen Series arise, from electronic
transitions from n = 3 and n = 4, 5, 6, etc. (infrared region).
Fig 2b.
-
Fig.3
Recognising energy level changes in a diagram (and how to construct
them!)
-
- Particular
changes are represented on
electronic energy level diagram Fig.3. For hydrogen, arrow ..
- represents the 4th line in
the 3rd series of the emission spectrum (n=7 to n=3),
- represents the 4th line in
the 2nd series of the absorption spectrum (n=2 to n=6),
- represents the 6th line in
the 1st series of the absorption spectrum (n=1 to n=7), and
- represents the 4th line of
the 1st series of the emission spectrum (n=5 to n=1)
- If the absorbed photon has enough energy, it can
remove the most loosely bound electron in a process called ionisation
...
- The 1st ionisation energy
(or enthalpy) is defined as the energy required to completely
remove the most weakly held electron from 1 mole of the gaseous atoms.
- e.g. for the process:
Na(g)
==> Na+(g) + e-
- this is the equation for the first
ionisation energy of sodium atoms
- ionisation is always
endothermic, heat absorbed ΔH = +493 kJ mol-1
- For hydrogen, this energy can be
calculated from the frequency of the light emitted or absorbed at the
conversion point in the
first series because it corresponds to the
quantum level change from n =1 to n = infinity or vice versa.
-
See Fig.1 for the first
series of lines of the hydrogen spectrum and the convergence point to
determine the frequency corresponding to ionisation and this value is
put into Planck's equation to calculate the 1st (and only) ionisation
energy of hydrogen,
E = h
calculations.
- Note that the lines in any series, for
any atom, tend to converge in the increasing frequency direction
because the energy levels converge in quantum level value the further
they are from the influence of the positive nucleus.
- The spectra of multi-electron
systems, from He onwards, are much more complex, but from spectroscopy a great
deal can be learned about their electronic structure, which aids our
understanding of an elements chemical behaviour.
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2.7 Evidence of quantum levels
from ionisation energies
Patterns
within a group and for an individual element
-
Evidence for
electronic 'shell structure' is obtained from spectroscopy and
ionisation energy measurements
-
Interpretations of graphs of the first and successive ionization
energies of the elements provides evidence for the
existence of the main quantum levels and the energy sub-levels too e.g.
-
(1) Ionisation energies
steadily decrease down a group
-
 e.g. for the process:
Na(g)
==> Na+(g) + e- etc.
-
Generally speaking the 1st energy
decreases down a group of the periodic table (see graph on the right
of the 1st ionisation energies of the group 1 and metals).
-
As you go down the group, each
element has an extra shell of occupied electronic energy levels
which shield the outermost and most loosely bound electron.
-
Therefore the most outer electron
is becoming further and further from the nucleus as the atom gets
bigger.
-
The further the electron (in the
s sub-shell) is from the nucleus, the less strongly it is held, so
less energy is required to remove it in the ionisation process.
-
This appears to outweigh the
effect of the increasing nuclear charge (Z) because the volume of
the atom is also expanding, allowing for the space required by the
orbitals of the extra shell of electrons.
-
Although this simple pattern
shows some feature of the group 1/2 atoms is steadily changing, I
wouldn't say it was the greatest evidence for the existence of
principal quantum levels ('shells').
-
(2) The patterns of the 1st
ionisation energies when plotted against atomic number (Z)
-
This graph does provide
substantial evidence of the principal quantum levels and directly
relates to the structure of the periodic table which was originally based on the
observed chemical properties of the elements.
-
The 1st ionisation energy,
and is the energy required to remove the most loosely bound electron from
one mole of the neutral
gaseous atom (it is always endothermic) e.g.
-
1st
IE of helium,
He(g) ==> He+(g) + e- (ΔH
= +2370 kJ mol-1 )
- this is the equation for the first
ionization energy of helium atoms.
- You write a similar equation for ANY
element of the periodic table.
-
The energy
required to remove the 2nd most loosely bound electron is called
the 2nd ionisation energy (first possible with helium),
which is therefore defined as the energy required to remove an
electron from one mole of the monopositive ions e.g. Na+,
but here we are just concerned with the first ionization energy.
-
-
Graph of periodic
ionization data for elements 1 to 38
above.
-
Generally speaking the 1st
ionisation energy increase from left to right across a period of the
periodic table.
-
As you go across the
period from one element to the next, the positive nuclear charge is
increasing by one unit as the atomic number increases by one unit and
the positive charge is acting on electrons in the same principal
quantum level.
-
The effective nuclear charge can be considered
to be equal to the number of outer electrons (this is very
approximate and NOT a rule) and this is increasing from left to
right as no new quantum shell is added
i.e. no extra shielding.
-
Therefore the outer electron is increasingly more strongly held by the
increasing positive charge of the nucleus and so,
increasingly, more energy is needed remove it.
-
BUT if the next 1st electron to
be removed from the next element is from a principal 'shell' of
electrons, it is much less strongly held, hence the minimum value
(as argued above). This occurs at atomic numbers 3, 11, 19, 37, 55
and 87 (alkali metals).
-
The highest values indicate the most stable
electron arrangements and these occur at atomic numbers 2, 10, 18,
36, 54 and 86 (noble gases). These numbers themselves indicate a
numerical pattern.
-
The 1st
ionisation energy (1st IE) pattern shows evidence ...
-
From the broad
periodic patterns of 1st IE, electrons are distributed in fixed
patterns of principal quantum levels,
-
The minimum ionisation
energies correspond to the first element in a period (group
1 alkali metal) and the peaks correspond to the last element
in a period (group 0/18 noble gas).
-
These two sets on
minimums and maximums correspond to 'new' sets of ionisation
energies in a 'new' principal quantum level.
-
BUT, that's not all the
graphs show ...
-
From the 'kinks' evidence of
sub-shells of electronic energy levels even within principal
quantum levels (see section
(3) below
on the two 'unexpected' decreases in ionisation energy in period
3.
-
You can also see
evidence of the d block of elements (3d shell) if you look at the pattern
of first ionisation energies of elements 1-38.
-
 (3)
Evidence from sub-levels - the 'kinks' in the 1st
ionization energy graph
-
In the 1st ionisation energy
graph you 'kinks' or abrupt decreases (e.g. Be to B, N to O,
Mg to Al and P to S) which provides evidence of sub-shells of
principal quantum levels. On the right, period 3 ionisation energies
are shown in more detail and you can clearly see this effect and its
similar for period 4.
-
To fully understand these two
'drops' in ionization energy, contrary to the period trend, you need to bring in your
hopefully gained electron configuration knowledge!
-
(i) A decrease from Mg
[1s22s22p63s2]
to Al [1s22s22p63s23p1]
Box spin diagram of 3s3p orbitals  
==> 
The anomalously low
value for aluminium is considered to be due to the first time a
3p electron is shielded by the full 3s sub–shell and, more
importantly, the 3p electron is a bit
further away (higher in energy) on average from the nucleus than the 3s electrons
(so less strongly bound), so less energy needed to remove it. The effect
to some extent overrides the effect of increasing proton number i.e. increase
in positive
nuclear charge from Mg to Al. However, after the kink, the
continued increase in nuclear charge ensures the Period 3 trend
for the 1st ionisation energy continues as expected until
sulfur, the 2nd anomaly.
-
(ii) A decrease from P
[1s22s22p63s23p3]
to S [1s22s22p63s23p4]
Box spin diagram of 3s3p orbitals 
==> 
Prior to the 4th 3p
electron, the other three p electrons occupy separate p
sub–orbitals (Hund's Rule of maximum multiplicity) to minimise
repulsion between adjacent orbitals. The
anomalously low values for sulphur is
considered to be due to the effect of the first pairing of
electrons in the 3p orbitals producing a repulsion
effect that to some extent overrides the effect of increasing proton
number (increase in positive nuclear charge), so less
energy needed to remove the 4th p electron. From the
'kink', the Period 3 trend for the 1st ionisation energy
continues as expected from sulfur to argon with increase in
nuclear charge.
-
(4) The consecutive ionisation enthalpies for the same element:
- e.g. for the process:
Na(g)
==> Na+(g) + e-
- this is the equation for the first
ionisation energy of sodium
- ionisation is always
endothermic, heat absorbed ΔH = +493 kJ mol-1
-
2nd IE of sodium,
Na+(g) ==> Na2+(g) + e- (ΔH
= +4562 kJ mol-1)
- this is the equation for the 2nd
ionisation energy of sodium and dramatically more endothermic.
- 3rd:
Na2+(g) ==> Na3+(g) + e- (ΔH
= +6940 kJ mol-1)
- 4th:
Na3+(g) ==> Na4+(g) + e- (ΔH
= +9540 kJ mol-1)
- etc. etc. and you can do the same for ANY
element of the periodic table until you run out of electrons to
be removed!
-
The graphs of ionisation versus
ionisation number (1st, 2nd, 3rd etc.) also provide evidence
'shells' of electrons, by looking for sudden extra large leaps in
the progressively increasing ionisation energy as each electron is
removed.
-
Successive ionisation energies
for a given element will always increase because less electrons are
being increasingly more strongly held nearer the nucleus by the
constant positive nuclear charge Z.
 |
IONISATION
ENERGY PATTERNS
 |
Spectra are not just used to elucidate details of electronic
quantum levels, but they are used in chemical analysis to identify and
quantitatively elements in a sample and by astronomers to identify elements in
distant objects like stars.
Examples of emission and absorption spectra are given at the end
of the page.
Emission spectra
The above diagram represents what happens on
excitation of an atom by an absorbed photon or other source of energy e.g. high
temperature in a hot bunsen flame (as in flame tests) or high voltage
discharge to vapourise and excite atoms between electrodes.
Electrons are excited to higher quantum level to
give an 'excited atom' state. - an unstable condition
An electron
in an excited atom, drops back down to a lower level and in doing so emits a
photon.
The energy of the photon ('quanta') will precisely match
the difference between two electronic energy quantum levels - from a
higher to a lower level - this is essence of quantum theory, the complex
mathematics of quantum mechanics came later!
So all the lines represent all the possible electronic transitions
giving a complex emission line spectrum - characteristic fingerprint for every
element.
For the visible region you observe a series of
coloured lines against a black background.
You can observe emission spectra from the chromosphere of our Sun
(~6000-20000oC).
Absorption spectra
If the visible spectrum of
white light is shone through gaseous atoms, particular wavelengths (of photons
of specific energy) are absorbed leaving 'black' lines in the spectrum.
The
photon's energy must match that required to move an electron from one energy
level to another higher level.
Again, the above diagram represents
what happens when electrons absorb photons to give the atom an excited state.
The energy of the photon must precisely match the
difference between two electronic energy quantum levels - from a lower
to a higher level.
For the visible region you observe a series of black
lines against the coloured spectrum background.
You can observe absorption spectra from the surface of our Sun (~5500oC).
|
A non–chemical test method for
identifying elements – atomic emission line spectroscopy
FLAME EMISSION SPECTROSCOPY - an instrumental method for elements from
high resolution line spectra
 If
the atoms of an element are heated to a very high temperature in a flame they emit
light of a specific set of frequencies (or wavelengths) called the
line spectrum. These are all
due to electronic changes in the atoms, the electrons are excited and
then lose energy by emitting energy as photons of light. Each line
represents one specific electron energy level change.
E
=
h
, E =
energy of a single photon (J),
h =
Planck's
Constant (6.63 x 10-34 JHz-1),
= frequency
(Hz).
The energy E, is for one photon interacting with one electron in one atom, so
E represents the difference in energy between the two electronic quantum
levels involved.
These emitted
frequencies can be recorded on a photographic plate, or these days a
digital camera.
Every element atom/ion has its own unique and particular set of electron
energies so each emission line spectra is unique for each element
(atom/ion) because of a unique set of electron level changes. This
produces a
different pattern of lines i.e. a 'spectral fingerprint' by which to
identify any element in the periodic table .e.g. the diagram on the left
shows some of the visible emission line spectra for the elements
hydrogen, helium, neon, sodium and mercury. Note
the double yellow line for sodium, hence the dominance of yellow in its
flame test colour. In fact the simple flame test colour observations for
certain metal ions relies entirely on the observed amalgamation of these
spectral lines. This is an example of an
instrumental chemical analysis called spectroscopy and is performed using an instrument
called an optical spectrometer (simple ones are called
spectroscopes). This method, called
flame emission
spectroscopy, is a fast and reliable method of chemical analysis.
This type of optical spectroscopy has enabled scientists to discover new
elements in the past and today identify elements in distant stars and
galaxies.
The alkali metals caesium (cesium) and rubidium were discovered by
observation of their line spectrum and helium identified from spectral
observation of our Sun. |
Examples of real emission spectra (from a
student handout in those happy days in 1965!)
Emission spectra hydrogen, helium, neon and sodium
Emission spectra
450 to 750 nm in the visible region (the white circles are from student
days in the 1960s!)
Note the brightest lines for sodium are in the
yellow
region - strongest emission above and strongest absorption below.
Therefore its not surprising in simple flame tests for
cations that sodium gives a bright yellow.
Note the visual difference for emission and
absorption spectra. I've redone more clearly the two spectra for sodium below.
Coloured lines for the emission spectrum against a
black background - from emitted photons due to electronic energy
level decreases in the sodium atoms.
Black lines for the absorption spectrum against a
visible spectrum background - from absorbed photons due to
electronic energy level increases in the sodium atoms.
Emission spectra for potassium, calcium, strontium and
barium
Emission spectra
450 to 750 nm in the visible region (the white circles are from student
days in the 1960s!)
You can relate these spectra to simple flame colour tests.
The lines for potassium don't seem to indicate a
lilac-purple flame test colour but look on the left and there a lot of
lines close together in the purple-violet region.
Calcium has many lines in the orange-red region and the
flame test colour is often quoted as 'brick red'.
Strontium gives lots of strong emission lines in the red
region and the flame colour is red.
Barium shows lots of strong emission lines right across
the visible spectrum and the flame colour seems to 'average' them all
out with a pale green - which is one of the strongest emission lines.
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ionisation energy patters, graphs and diagrams of group and period
patterns in ionisation energies explained, explaining the origin of emission
and absorption spectra of elements and use for identification
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Bohr's atomic model
