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)