Download - Energy Levels and Transitions in Atoms
ENERGY LEVELS AND TRANSITIONS IN ATOMS ENERGY LEVELS IN ATOM
Generally, atoms consist of a positive nucleus surrounded by a cloud of negative electrons. Each
electron in the cloud may possess only very specific amounts of energy. The total electronic energy of
the atom is the sum of the energies of all its individual electrons. If the electronic energy of the atom is
such that it contains only the minimum allowed energy, the atom is said to be in the "ground state." If
the total energy content of the atom is greater than the ground state energy, the atom is said to be in
an "excited state."
Figure 1 is a partial energy level diagram for a mercury atom. The ground state is the energy level
denoted as E1. When in this state, the atom has an electronic energy labelled as zero. This zero does
not mean that the atom contains no energy but, rather, that it contains its minimum allowable energy
and that no electronic energy can be removed from it.
Fig. 1 of mercury Some energy levels\
The higher energy levels indicated (E2, E3, etc.) indicate specific amounts of energy that the atom may
contain. Each of these levels corresponds to a particular configuration for the electrons around the
nucleus of the atom. In general, an electronic configuration which, on the average, has its electrons
further removed from the nucleus than others, will possess a higher energy state, hence a higher
atomic energy level in Figure 1. A single atom may occupy only one of these energy levels at any one
instant. In order to move from one energy level to another, the atom must gain or lose an amount of
energy exactly equal to the energy difference between the two levels. Such a change in energy
level such—as that shown by the arrows in Figure 1 from E5 to E2 or E1 to E8—is called an "atomic
transition," and this change may occur in several ways.
An atom in an excited state—that is, any state above the ground state—will not remain there
indefinitely. Atoms tend to release their excess energy and return to the ground state or by a series of
transitions to successively lower energy levels, ending at the ground state. The atomic lifetime of a
particular energy state is the time required for half of the atoms initially in that state to make a
downward transition without benefit of outside influence (such as stimulated emission). For example
if 1012 mercury atoms were initially in energy state E6 of Figure 1, only 5 x 1011 atoms would remain
in that state after a time interval equal to the atomic lifetime of that state. The atomic lifetime,
therefore, is a measure of the rate at which atoms leave a given energy level by releasing some of their
energy. The average atomic lifetime is about 10–8 seconds, but there are large variations. Atomic
lifetimes may be as short as 10–11 sec or as long as 10–2 sec. Energy states having atomic lifetimes of
10–6 sec or longer are called "metastable states."
SPONTANEOUS EMISSION OF A PHOTON
One way for an atom to make a transition from a particular energy level to a lower energy state is by a
process known as "spontaneous emission." This type of emission occurs when the atom releases a
photon possessing an energy equivalent to the energy difference between the two energy levels in
question. The photon is emitted without benefit of an external stimulus and travels away from the
point of emission in a random direction. The frequency and wavelength of the photon are, of course, a
function of the energy of the emitted photon.
RADIATIONLESS TRANSITIONS
In some cases, atoms make downward transitions without releasing a photon. When this occurs, the
energy released by the atom must be carried away in some form other than emitted electromagnetic
radiation. Such a transition is called a "radiationless transition."
In gases, radiationless transitions occur when an excited atom collides with an atom in some lower
energy state. A portion of the energy of the more energetic atom is transferred to the less energetic
atom during the collision. One atom loses a certain amount of energy while the other atom absorbs the
energy lost by the more energetic atom. In this manner, the energy is released by an atom, making the
downward transition without the production of a photon.
In solids, radiationless transitions often account for a temperature increase within the material. The
energy released by an atom in a downward transition appears as other (e.g., vibrational) energy in the
area surrounding the atom's equilibrium position in the solid. This vibrational energy increases the
thermal energy in the solid and, thus, raises its temperature.
ABSORPTION OF A PHOTON BY AN ATOM
Under certain conditions, atoms can absorb the same wavelengths of light that they emit through
spontaneous emission. A case in point is illustrated in Figure 2.
Fig. 2 Absorption of light
An atom initially in energy state E1 is struck by a photon of energy Ep = E3 – E1. The photon ceases to
exist, and the atom makes an upward transition to level E3. The photon's energy now is contained in
the excited atom in the E3 energy level. For this type of photon absorption by an atom to occur, two
conditions must be satisfied:
• The energy of the incoming photon must be equivalent to the energy difference between the
two energy levels in question.
• The atom absorbing the photon must be in the lower of the two energy levels.
Thus, an atom in level E1 in Figure 2 could absorb a photon of energy (E2 – El), (E3 – E1), or (E4 – E1),
but it could not absorb a photon of energy (E4 – E2) or (E3 – E2).
STIMULATED EMISSION
Figure 3 illustrates the stimulated emission process that produces laser light. The conditions
necessary for stimulated emission to occur are the same as those for absorption, except that the
emitting atom must be in the upper of the two energy states involved. In the case of stimulated
emission, the incident photon stimulates the atom to release a photon sooner than it would have in
the absence of an external stimulus, as in spontaneous emission. In this case, the photon released by
the stimulated atom has the same energy, frequency, wavelength, phase and direction of travel as the
incident stimulating photon. The photon emitted by the stimulated atom is also in phase with the
incident photon, and the energies of both photons are added together in the resultant beam. This, or
course, is the process at the heart of laser action.
Fig. 3 Stimulated emission of light
Emission Spectra for Atomic Gases
To observe an emission spectrum, one creates an electric discharge in a closed, transparent tube which
contains the gas, thereby causing the gas to glow or fluoresce. This fluorescent light is sent through a
well-defined, narrow entrance slit of a spectrometer. The spectrometer, with the help of prisms or
gratings, forms separate images of the entrance slit on a photographic plate, depending on the
different wavelengths of fluorescent light passing through the slit. A typical setup designed to observe
the emission spectrum for neon gas, for example, is shown in Figure 4a. The line images formed on the
plate are shown in Figure 4b. In Figure 4c, the same line images are shown, appropriately coloured
according to their actual wavelengths, just as they would be seen by the naked eye.
The formation of emission spectra and their relationship to the energy levels characteristic of the
atomic gases is not hard to understand. The energy provided by the electric discharge is absorbed by
the atoms in the gas, causing them to be raised to higher energy levels—levels such as E2, E3, E4 and so
on in Figure 1. Once the atoms reach the various higher energy levels, they begin to fall back to lower
levels via the process of spontaneous emission. (It is the spontaneous emission that we see as the tube
glows or fluoresces.) As the atoms fall back—say from level E8 to E7, or E7 to E4, or E4 to E1, or directly
from E8 to E1—they emit photons with energies equal to E8 – E7, E7 – E4, E4 – E1, E8 – E1and so on. Since
we know that l = hc/E, we see that, for each transition, a photon of different wavelength is created.
When these emitted photons—arising from the downward energy transitions in the excited gas—are
sent through the entrance slit of a spectrometer, they form separate, distinct images of the
spectrometer slit on the photographic plate. If we have known wavelengths of calibration lines on the
plate, we can calculate the wavelength of the test-gas lines, and work back to get the energy
differences and finally the various energy levels for the test gas. In this way we establish the energy
level diagrams—the emission spectra—which characterize the various atomic gases such as
hydrogen, helium, neon, etc.
A closer look at the line images on the plate shows that they are not all equally bright. Some are
lighter, some are darker. An analysis of the "intensity" of each line formed on the plate gives us
important information about the probability for a transition between the various energy levels. For
example, if a certain line, say that for the transition from E8 to E1, is much more intense than the line
for the transition from E8 to E4, then the transition probability for spontaneous emission from E8 to
E1 is higher than that from E8 to E4.
Absorption Spectra for Atomic Gases
The process for observing absorption spectra is similar to that for observing emission spectra. In this
case one places the atomic gas under study in a transparent, cylindrical container and passes a
collimated, white-light beam through the container. The light beam emerging from the cylinder is then
analysed by a spectrometer, with the absorption lines showing up on a photographic plate. The lab
setup is shown schematically in Figure 5.
In absorption spectra, the photographic plate would be uniformly exposed (darkened) due to the
white light, except at positions where the particular wavelengths in the white light are absorbed by
the gas. For those absorbed wavelengths, no light reaches the plate, and at those positions the plate
"registers" line images for the "absent" light.
Since "white" light contains all wavelengths in the visible spectrum, a continuum from 400 nm to
700 nm, the beam incident on the atomic gas contains a continuum of photon energies, from 1.77 eV
(for l = 700 nm) to 3.10 eV (for l = 400 nm). For each photon in the beam, for which a match between
the photon energy and an energy level difference in the atomic gas exists, the photon is absorbed and
disappears from the beam. All other photons continue on through the spectrometer and expose the
photographic plate. The absorbed photons, with their tell-tale wavelengths, never reach the plate, so
the plate remains unexposed at those particular wavelengths—resulting in white lines on a dark
background. When the plate is developed and a positive print is made from the negative, the spectrum
appears with black lines on a white background. Identifying the wavelengths of these lines and
working back to establish the energy level differences for the atomic gas, we develop the energy level
diagram characteristic of that gas, just as was done with emission spectra.
Fig. 6 Line spectrum of a monatomic atom
Again, the intensity of the various lines on the photographic plate provides evidence for the transition
probability. An intensity analysis of the absorption lines-performed with an optical instrument called
a densitometer- yields a trace such as that shown in Figure 6. Here the line emission intensity is
plotted against wavelength for the line spectra. In the trace, the higher the peaks, the more probable
the transition and the shorter the lifetime of the energy state involved. Similarly, the lower the peaks,
the less probable the transition and the longer the lifetime of the state involved.
EMISSION AND ABSORPTION SPECTRA ATOMIC GASES
Figure 4 represents the typical emission spectrum of a monatomic gas, such as helium or neon. This
type of spectrum is produced by an electrical discharge passed through a gas sample contained at low
pressure. Each of the lines in the emission spectrum is produced by a single atomic transition, and the
intensity of each line produced is dependent upon the probability of atoms making that particular
transition. Stronger lines are the result of the most probable transitions from energy states having
short atomic lifetimes. Weaker lines are produced by transitions from states that have long atomic
lifetimes or by low-probability transitions that compete with the higher-probability transitions.
Each of the lines within the line spectrum (Figure 6) actually consists of a narrow range of
wavelengths (Figure 7), which is the result of a phenomenon called "Doppler broadening."
Fig. 7 Width of a spectral line
As illustrated in Figure 8, stationary atoms emit light of a wavelength l0, corresponding to the center
of the spectral line, although moving atoms may emit slightly different wavelengths because of their
motion. If a moving atom emits a photon in the same direction of travel as the atom, the wavelength
(l1) will be slightly shorter (frequency higher) than the wavelength emitted by a stationary atom. In
contrast, if the moving atom emits a photon traveling in a direction opposite to the atom's motion, the
wavelength (l2) will be longer (frequency lower). Thus, the additive result for a large collection of
atoms is the Doppler broadened line of Figure 5. The line center energy corresponds to the exact
difference in energies of the two electronic states involved in the transition for stationary atoms or
atoms moving in the same direction at the same velocity.
Fig. 8 The Doppler effect.
SOLIDS
Figure 9 represents the trace of an absorption spectrum for a solid material. Unlike the comparatively
narrow spikes of a gaseous spectrum, this spectrum consists of broad, irregularly-spiked regions
called absorption bands. This difference in spectral character is due to the fact that the energy levels
of an atom bound in a solid shift slightly in the ever-present local electric and magnetic fields. Each
atom bound within a material produces electric and magnetic fields as a characteristic of the atom's
nature; consequently, when large numbers of atoms are crowded close together in a solid, the energy
levels of each atom shift because of the fields produced by all its neighbours. This wholesale shifting of
energy levels broadens all the spectral lines. Areas containing a closely-spaced group of strong lines
appear as an absorption band. In crystalline solids such as Nd:YAG (Nd atoms in yttrium aluminium
garnet), these absorption bands consist of groups of sharp-edged lines. In solids such as Nd:glass
which lack an ordered crystal structure, the bands are broader and less distinct. The definitions of
these absorption bands are important in determining the manner of optical exciting solid-state lasers.
Fig. 9 Absorption spectrum of a solid
Resolution (Width) Lines Spectra
Atomic spectral lines have finite widths with factors to line broadening due to:
• Natural Broadening - The lifetime of
the excited states lead to uncertainty
leading to broadening due to shorter
excited state lifetimes. Lifetimes of 10-
8 s lead to width of 10-5 nm.
• Collisional Broadening -Also
referred to as Pressure Broadeningis
the result of collision of the excited
state leads to shorter lifetimes and
broadening of the spectral lines.
• Doppler Broadening - When
molecules are moving towards a
detector or away from a detector the
frequency will be offset by the net
speed the radiation hits the detector.
This is also known as the Doppler
effect and the true frequency will
ether be red shifted (if the chemical is
moving away from the detector) or
blue shifted (if the chemical is moving
towards the detector)