Lecture 4

The Atom : Spectroscopy, Lasers and the Periodic Table

Bohr's successful model of the atom was obviously a tremendous breakthrough. It not only provided a solution to the question of the atom's stability (and in doing so put the quantization ideas onto firmer and firmer grounds), and explained the origin of the spectral lines, but effectively it "brought light" to the whole issue of the nature and origin of light: what our eyes detect as light is nothing but a continuous dance of electrons, jumping back and forth between allowed atomic levels.....

It is interesting to note how the eye has evolved to be sensitive, among the whole spectrum of ElectroMagnetic radiation, just to the energies corresponding to such electron transitions...One might wonder for instance why the eye is not capable of detecting e.g. infrared radiation....

Before we proceed, it might be useful to introduce a new unit for the measurement of energies, which is particularly useful and intuitive when dealing with electrons and other elementary particles.

As we have seen, energy can assume many different forms (mechanical, thermal, electric, etc.) and, even though the standard unit for energy is the Joule, in different environments other units (calorie, Btu, kilowatthour) are more directly useful.

When dealing with electrons, etc., a very practical unit for energy is the electron-volt, eV.

Definition of eV : an electron acquires the energy of 1 eV when it travels across the difference of potential of 1 Volt.

It would be easy to prove that visible photons ($\lambda \sim$ 400-600 nm) have energies of a few eV's. In other words : energies characteristic of atomic transition producing visible light are rather low, typically of the order of what can be obtained with a small battery.

Let us now return to atomic spectra: as we have seen, each element, when excited, will emit light in a set of well defined lines (colours), unique to the element itself (note that the same is true also for compounds, not just for elements). According to Bohr's theory, also the converse is true, i.e. a given substance can only absorb energy at the values corresponding to the emission. Both these factors are exploited in a wide range of applications, based upon the techniques of spectroscopy.
[0.2in] Emission Spectroscopy : one can detect the presence of an element in a given substance, even if it cannot handle it directly, by observing the spectrum of the light emitted by the substance. Presence of the element will be revealed by the spectral "fingerprints". In this way, for instance, astrophysicists can study the composition of the stars.

Absorption Spectroscopy : similarly, one can detect the presence of a given element by observing whether specific light frequencies are absorbed. Suppose you start with white light, i.e. with light containing a wide range of frequencies covering the whole visible spectrum, and you send such light through, e.g., Helium gas : the Helium will be able to absorb light only at the frequencies corresponding to its own atomic levels. Such frequencies will then be absorbed by the gas, and will therefore be missing from the original white light spectrum.

QUESTION : An atom's first three levels correspond to energies of 0, 10 and 20 eV respectively. What will happen to an electron sitting in the lowest level when a 15 eV photon goes by?

A the electron will jump to the next higher level, and a 5 eV photon will be emitted to account for the difference


B the electron will jump to the second higher level, and a 5 eV photon will be absorbed to account for the difference


C the electron will jump to the next higher level, no extra photons will be absorbed or emitted


D nothing will happen, the electron will stay where it is


E not enough information, need to know the actual frequencies of the photons involved


F I have no idea what this guy is talking about

We should now have enough knowledge to understand how Lasers work:
[0.2in] Laser : Light Amplification by Stimulated Emission of Radiation

(and, for your information, scientists have also produced Masers, Microwave Amplification etc.)

For practical purposes, Lasers produce a very intense, very well collimated, monochromatic (i.e of a single colour/frequency) beam of light.

Lasers are being utilized in a very wide array of applications, the specific application depending upon the beam's characteristics (typically, its power):

• optical scanners (supermarket check-out), classroom pointers
• land survey, land movements
• holography (3D imaging)
• precision surgery
• cutting and welding
• "Star Wars" (SDI) weapons
• atomic and molecular research (pure and applied)
• etc. etc.

How do Lasers work?

The basic principle behind the Laser's operation is the one of stimulated emission. Einstein predicted such an effect as early as 1917, but the practical realization had to wait until the late 50's to early 60's.

Stimulated emission : let's suppose that we have an atom of a given material with an electron sitting in some excited orbit. Typically, such an electron will eventually fall down to the lower orbit, by emitting a photon of the appropriate frequency, but it is not possible to predict when such a transition will take place. Let us now suppose that a photon of exactly the correct energy (i.e. the energy corresponding to the difference between the excited and the lower orbit) is whizzing by: the presence of this photon will induce (stimulate) the electron's transition into the lower orbit. Notice the the photon going by is not affected, it only acts as a "mediator" ; the net effect is that, where originally we had one photon, now we have two.

Another important point is that the stimulated photon is emitted "in phase" with the stimulating one, this will therefore lead to constructive interference.

Let us now suppose that in the material there was not just one, but many electrons in the excited state : as soon as one photon causes stimulated emission, two photons are going by, and they will in turn stimulate more emissions, so that we have four photons, then eight.....

Still, this process would soon come to an end, unless there was some way to bring the electrons back to the excited state. This process is called pumping, and is achieved by means of some external energy source, e.g. an electric current (note then that a Laser needs some power source to operate). With suitable pumping, a Laser can therefore produce a continuous beam of the desired properties.

The other basic component of the Laser is given by the two end-wall mirrors : these mirrors will keep the photon bouncing back and forth, in order to boost the effect of each single photon. At one end, the mirror will be made to be 95% reflecting and 5% transmitting, so that a fraction of the photons will escape to form the actual Laser beam.

Atomic Electron Shells and the Periodic Table

From what we have seen, orbiting electrons determine the optical properties of any given material. Next we will see how they also control the chemical properties of the elements, and what are the facts forming the base for the regularities (and the particular features) of the Periodic Table of Elements.

So far, you have been told that, for each element, there is only a set of specific orbits that the electron can occupy. The study of Quantum Mechanics and its implications showed another fact :

for each orbit, there is only a finite number of positions that can be occupied by an electron. Once all of the allowed spaces in a given orbit are occupied, further electrons will have to position themselves in an outer orbit (think of a multi-level parking garage, when the first level is full you have to look for space in the higher levels....).

To use the correct Quantum Mechanics terms: the ensemble of electrons that can occupy a given orbit is called a shell. Within a shell, what we just called a "position" is usually referred to as a state. The principle introduced above can then be restated as :

in any given shell, no two electrons can be in the same state (this is referred to as Pauli exclusion principle).

Guided by this principle, we can know interpret the Periodic Table. The other piece of information we need is how many states there are in each shell. Quantum Mechanics provides the answer :

Shell 1 : 2 states

Shell 2 : 8 states

Shell 3 : 8 states

After that it becomes more complicated, but the effect of these rules onto the periodic table is obvious, especially if we take into account that, as we'll understand better in future lectures, the chemical properties of each element depend mainly on the number of electrons in the outermost shell.