Ch 5 Modern physics
References
1- College physics, Serway, e 7
2- websites
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1-Introduction
Attempts to explain the behavior of matter on the atomic level with the laws of classical
physics were consistently unsuccessful. Various phenomena, such as the electromagnetic
radiation emitted by a heated object (blackbody radiation), the emission of electrons by
illuminated metals (the photoelectric effect), and the emission of sharp spectral lines by
gas atoms in an electric discharge tube, Figure 1, couldn’t be understood within the
framework of classical physics. Between 1900 and 1930, however, a modern version of
mechanics called quantum mechanics or wave mechanics was highly successful in
explaining the behavior of atoms, molecules, and nuclei
Figure 1 Visible spectra. (a) Line spectra produced by emission in the visible range for the elements hydrogen, mercury, and neon. (b)
The absorption spectrum for hydrogen. The dark absorption lines occur at the same wavelengths as the emission lines for hydrogen
shown in (a).
At the beginning of the 20th century, scientists were taken by the failure of classical
physics to explain the characteristics of spectra. Why did atoms of a given element emit
only certain lines? Further, why did the atoms absorb only those wavelengths that they
emitted? In 1913 Bohr provided an explanation of atomic spectra that includes some
features of the currently accepted theory. Using the simplest atom, hydrogen, Bohr
developed a model of what he thought must be the atom’s structure in an attempt to explain
why the atom was stable. His model of the hydrogen atom contains some classical features,
as well as some revolutionary postulates that could be justified within the framework of
modern physics. The basic assumptions of the Bohr Theory as it applies to the hydrogen
atom are as follows:
1. The electron moves in circular orbits about the proton under the influence of the
Coulomb force of attraction, as in the Figure. The Coulomb force produces the
electron’s centripetal acceleration, Figure 1.
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2. Only certain electron orbits are stable. These are orbits in which the hydrogen atom
doesn’t emit energy in the form of electromagnetic radiation. Hence, the total energy of the
atom remains constant, and classical mechanics can be used to describe the electron’s
motion.
3. Radiation is emitted by the hydrogen atom when the electron “jumps” from a more
energetic initial state to a less energetic state. The “jump” can’t be visualized or treated
classically. In particular, the frequency f of the radiation emitted in the jump is related to
the change in the atom’s energy and is independent of the frequency of the electron’s
orbital motion. The frequency of the emitted radiation is given by
Ei - Ef = hf
where Ei is the energy of the initial state, Ef is the energy of the final state, h is Planck’s
constant, and Ei > Ef .
4. The size of the allowed electron orbits is determined by a condition imposed on the
electron’s orbital angular momentum: the allowed orbits are those for which the electron’s
orbital angular momentum about the nucleus is an integral multiple of h (pronounced “h
bar”), where :
mevr = nh,
n=1,2,3,….
The Bohr theory of the hydrogen atom was a tremendous success in certain areas because it
explained several features of the hydrogen spectrum that had previously defied explanation.
Once a basic model is constructed, refinements and modifications can be made to enlarge
on the concept and to explain finer details.
2- ATOMIC TRANSITIONS
We have seen that an atom will emit radiation only at certain frequencies that correspond to
the energy separation between the various allowed states. Consider an atom with many
allowed energy states, labeled E1, E2, E3, . . . , as in Figure 2.
Figure 2 Energy level diagram of an atom with various allowed states. The lowest energy state, E 1, is the ground state. All others are
excited states.
When light is incident on the atom, only those photons whose energy hf matches the energy
separation E between two levels can be absorbed by the atom. A schematic diagram
representing this stimulated absorption process is shown in Figure 3.
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Figure 3 Diagram representing the process of stimulated absorption
of a photon by an atom. The blue dot represents an electron
The electron is transferred from the ground state to the excited state
when the atom absorbs a photon of energy hf = E2 - E1
Figure 4 Diagram representing the process of spontaneous
emission of a photon by an atom that is initially in the excited
state E2. When the electron falls to the ground state, the atom of
emits a photon energy hf = E2 - E1.
At ordinary temperatures, most of the atoms in a sample are in the ground state. If a vessel
containing many atoms of a gas is illuminated with a light beam containing all possible
photon frequencies (that is, a continuous spectrum), only those photons of energies E2- E1,
E3- E1, E4 -E1, and so on, can be absorbed. As a result of this absorption, some atoms are
raised to various allowed higher energy levels, called excited states. Once an atom is in an
excited state, there is a constant probability that it will jump back to a lower level by
emitting a photon, as shown in Figure 4. This process is known as spontaneous emission.
Typically, an atom will remain in an excited state for only about 10-8 s.
A third process that is important in lasers, stimulated emission, was predicted by Einstein
in 1917. Suppose an atom is in the excited state E2, as in Figure 5, and a photon with
energy hf = E2 - E1 is incident on it. The incoming photon increases the probability that the
excited atom will return to the ground state and thereby emit a second photon having the
same energy hf. Note that two identical photons result from stimulated emission: the
incident photon and the emitted photon. The emitted photon is exactly in phase with the
incident photon. These photons can stimulate other atoms to emit photons in a chain of
similar processes. The many photons produced in this fashion are the source of the intense,
coherent (in-phase) light in a laser.
Figure 5 Diagram representing the process of stimulated emission of a photon by an incoming photon of energy hf. Initially, the atom is
in the excited state. The incoming photon stimulates the atom to emit a second photon of energy hf = E2 - E1.
3- LASERS
We have described how an incident photon can cause atomic transitions either upward
(stimulated absorption) or downward (stimulated emission). The two processes are equally
probable. When light is incident on a system of atoms, there is usually a net absorption of
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energy, because when the system is in thermal equilibrium, there are many more atoms in
the ground state than in excited states.
However, if the situation can be inverted so that there are more atoms in an excited state
than in the ground state, a net emission of photons can result. Such a condition is called
population inversion. This is the fundamental principle involved in the operation of a laser,
an acronym for light amplification by stimulated emission of radiation. The amplification
corresponds to a buildup of photons in the system as the result of a chain reaction of events.
The following three conditions must be satisfied in order to achieve laser action:
1. The system must be in a state of population inversion (that is, more atoms in an excited
state than in the ground state).
2. The excited state of the system must be a metastable state, which means its lifetime must
be long compared with the otherwise usually short lifetimes of excited states. When that is
the case, stimulated emission will occur before spontaneous emission.
3. The emitted photons must be confined within the system long enough to allow them to
stimulate further emission from other excited atoms. This is achieved by the use of
reflecting mirrors at the ends of the system. One end is totally reflecting, and the other is
slightly transparent to allow the laser beam to escape.
One device that exhibits stimulated emission of radiation is the helium–neon gas laser.
Figure 6 is an energy-level diagram for the neon atom in this system.
The mixture of helium and neon is confined to a glass tube sealed at the ends by mirrors. A
high voltage applied to the tube causes electrons to sweep through it, colliding with the
atoms of the gas and raising them into excited states. Neon atoms are excited to state E3*
through this process and also as a result of collisions with excited helium atoms. When a
neon atom makes a transition to state E2, it stimulates emission by neighboring excited
atoms. This results in the production of coherent light at a wavelength of 632.8 nm
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Figure 7 Energy-level diagram for the neon atom in a helium–neon laser. The atom emits 632.8-nm photons through stimulated
emission in the transition E3 - E2. This is the source of coherent light in the laser.
. Figure 7 summarizes the steps in the production of a laser beam.
Figure 7 (a) Steps in the production of a laser beam. The tube contains atoms, which represent the active medium. An external source of
energy (optical, electrical, etc.) is needed to “pump” the atoms to excited energy states. The parallel end mirrors provide the feedback of
the stimulating wave
Since the development of the first laser in 1960, laser technology has exhibited tremendous
growth. Lasers that cover wavelengths in the infrared, visible, and ultraviolet regions of the
spectrum are now available. Applications include the surgical “welding” of detached
retinas, “lasik” surgery, precision surveying and length measurement, a potential source for
inducing nuclear fusion reactions, precision cutting of metals and other materials, and
telephone communication along optical fibers. These and other applications are possible
because of the unique characteristics of laser light. In addition to being highly
monochromatic and coherent, laser light is also highly directional and can be sharply
focused to produce regions of extremely intense light energy.
The word laser started as an acronym for "light amplification by stimulated emission of
radiation", where "light" broadly denotes electromagnetic radiation of any frequency, not
only visible light; hence infrared laser, ultraviolet laser, X-ray laser, and so on. Because the
microwave predecessor of the laser, the maser, was developed first, devices of this sort
operating at microwave and radio frequencies are referred to as "masers" rather than
"microwave lasers" or "radio lasers".
Assignment
Describe the operation of a helium–neon laser. Include a description of the method for
obtaining the inverted population distribution.
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