Q5. How did the quantum theory of light come about?
It did not arise from any attempt to
explain the behavior of light itself; by 1890 it was generally accepted
that the electromagnetic theory could explain all of the properties of
light that were then known.
Certain aspects of the interaction between
light and matter that were observed during the next decade proved rather
troublesome, however. The relation between the temperature of an object
and the peak wavelength emitted by it was established empirically by
Wilhelm Wien in 1893. This put on a quantitative basis what everyone
knows: the hotter the object, the "bluer" the light it emits.
Q6. What is black body radiation?
All objects above the temperature of
absolute zero emit electromagnetic radiation consisting of a broad range
of wavelengths described by a distribution curve whose peak wavelength for
a "perfect radiator" known as a black body is given by Wien's
ordinary temperatures this radiation is entirely in the infrared region of
the spectrum, but as the temperature rises above about 1000K, more energy
is emitted in the visible wavelength region and the object begins to glow,
first with red light, and then shifting toward the blue as the temperature
This type of radiation has two important
characteristics. First, the spectrum is a continuous one, meaning that all
wavelengths are emitted, although with intensities that vary smoothly with
wavelength. The other curious property of black body radiation is that it
is independent of the composition of the object; all that is important is
Q7. How did black body radiation lead to
Black body radiation, like all
electromagnetic radiation, must originate from oscillations of electric
charges which in this case were assumed to be the electrons within the
atoms of an object acting somewhat as miniature Hertzian oscillators. It
was presumed that since all wavelengths seemed to be present in the
continuous spectrum of a glowing body, these tiny oscillators could send
or receive any portion of their total energy. However, all attempts to
predict the actual shape of the emission spectrum of a glowing object on
the basis of classical physical theory proved futile.
In 1900, the great German physicist Max
Planck (who earlier in the same year had worked out an empirical formula
giving the detailed shape of the black body emission spectrum) showed that
the shape of the observed spectrum could be exactly predicted if the
energies emitted or absorbed by each oscillator were restricted to
integral values of hn, where n is the frequency and h is a constant 6.626E34 J s
which we now know as Planck's Constant. The allowable energies of each
oscillator are quantized, but the emission spectrum of the body remains
continuous because of differences in frequency among the uncountable
numbers of oscillators it contains.This modification of classical theory,
the first use of the quantum concept, was as unprecedented as it was
simple, and it set the stage for the development of modern quantum
Q8. What is the photoelectric effect?
Shortly after J.J. Thompson's experiments
led to the identification of the elementary charged particles we now know
as electrons, it was discovered that the illumination of a metallic
surface by light can cause electrons to be emitted from the surface. This
phenomenon, the photoelectric effect, is studied by illuminating one of
two metal plates in an evacuated tube. The kinetic energy of the
photoelectrons causes them to move to the opposite electrode, thus
completing the circuit and producing a measurable current. However, if an
opposing potential (the retarding potential) is imposed between the two
electrons, the kinetic energy can be reduced to zero so that the electron
current is stopped. By observing the value of the retarding potential Vr,
the kinetic energy of the photoelectrons can be calculated from the
electron charge e, its mass m and the frequency
of the incident light:
Q9. What peculiarity of the photoelectric
effect led to the photon?
Although the number of electrons ejected
from the metal surface per second depends on the intensity of the light,
as expected, the kinetic energies of these electrons (as determined by
measuring the retarding potential needed to stop them) does not, and this
was definitely not expected. Just as a more intense physical disturbance
will produce higher energy waves on the surface of the ocean, it was
supposed that a more intense light beam would confer greater energy on the
photoelectrons. But what was found, to everyone's surprise, is that the
photoelectron energy is controlled by the wavelength of the light, and
that there is a critical wavelength below which no photoelectrons are
emitted at all.
Albert Einstein quickly saw that if the
kinetic energy of the photoelectrons depends on the wavelength of the
light, then so must its energy. Further, if Planck was correct in
supposing that energy must be exchanged in packets restricted to certain
values, then light must similarly be organized into energy packets. But a
light ray consists of electric and magnetic fields that spread out in a
uniform, continuous manner; how can a continuously-varying wave front
exchange energy in discrete amounts? Einstein's answer was that the energy
contained in each packet of the light must be concentrated into a tiny
region of the wave front. This is tantamount to saying that light has the
nature of a quantized particle whose energy is given by the product of
Planck's constant and the frequency:
Einstein's publication of this explanation
in 1905 led to the rapid acceptance of Planck's idea of energy
quantization, which had not previously attracted much support from the
physics community of the time. It is interesting to note, however, that
this did not make Planck happy at all. Planck, ever the conservative, had
been reluctant to accept that his own quantized-energy hypothesis was much
more than an artifice to explain black-body radiation; to extend it to
light seemed an absurdity that would negate the well-established
electromagnetic theory and would set science back to the time before
Q10. Where does relativity come in?
Einstein's special theory of relativity
arose from his attempt to understand why the laws of physics that describe
the current induced in a fixed conductor when a magnet moves past it are
not formulated in the same way as the ones that describe the magnetic
field produced by a moving conductor. The details of this development are
not relevant to our immediate purpose, but some of the conclusions that
this line of thinking led to very definitely are. Einstein showed that the
velocity of light, unlike that of a material body, has the same value no
matter what velocity the observer has. Further, the mass of any material
object, which had previously been regarded as an absolute, is itself a
function of the velocity of the body relative to that of the observer
(hence "relativity"), the relation being given by
in which mo is the rest mass of
the particle, v is its velocity with respect to the observer, and c is the
velocity of light.
According to this formula, the mass of an
object increases without limit as the velocity approaches that of light.
Where does the increased mass come from? Einstein's answer was that the
increased mass is that of the kinetic energy of the object; that is,
energy itself has mass, so that mass and energy are equivalent according
to the famous formula
The only particle that can move at the
velocity of light is the photon itself, due to its zero rest mass.
Q11. Can the mass-less photon have
Although the photon has no rest mass, its
energy, given by , confers upon it an effective mass of
and a momentum of
Q12. If waves can be particles, can
particles be waves?
In 1924, the French physicist Louis de Broglie
proposed (in his doctoral thesis) that just as light possesses
particle-like properties, so should particles of matter exhibit a
wave-like character. Within two years this hypothesis had been confirmed
experimentally by observing the diffraction (a wave interference effect)
produced by a beam of electrons as they were scattered by the row of atoms
at the surface of a metal.
de Broglie showed that the wavelength
of a particle is inversely proportional to its momentum:
Notice that the wavelength of a stationary
particle is infinitely large, while that of a particle of large mass
approaches zero. For most practical purposes, the only particle of
interest to chemistry that is sufficiently small to exhibit wavelike
behavior is the electron (mass 9.11E31 kg).
Q13. Exactly what is it that is
We pointed out earlier that a wave is a
change that varies with location in a periodic, repeating way. What kind
of a change do the crests and hollows of a "matter wave" trace
out? The answer is that the wave represents the value of a quantity whose
square is a measure of the probability of finding the particle in that
particular location. In other words, what is "waving" is the
value of a mathematical probability function.
Q14. What is the uncertainty principle?
In 1927, Werner Heisenberg proposed that
certain pairs of properties of a particle cannot simultaneously have exact
values. In particular, the position and the momentum of a particle have
associated with them uncertainties x
As with the de Broglie particle
wavelength, this has practical consequences only for electrons and other
particles of very small mass. It is very important to understand that
these "uncertainties" are not merely limitations related to
experimental error or observational technique, but instead they express an
underlying fact that Nature does not allow a particle to possess definite
values of position and momentum at the same time. This principle (which
would be better described by the term "indeterminacy" than
"uncertainty") has been thoroughly verified and has far-reaching
practical consequences which extend to chemical bonding and molecular
Q15. Is the uncertainty principle
consistent with particle waves?
Yes; either one really implies the other.
Consider the following two limiting cases: · A particle whose velocity is
known to within a very small uncertainty will have a sharply-defined
energy (because its kinetic energy is known) which can be represented by a
probability wave having a single, sharply-defined frequency. A
"monochromatic" wave of this kind must extend infinitely in
But if the peaks of the wave represent
locations at which the particle is most likely to manifest itself, we are
forced to the conclusion that it can "be" virtually anywhere,
since the number of such peaks is infinite! · Now think of the opposite
extreme: a particle whose location is closely known. Such a particle would
be described by a short wavetrain having only a single peak, the smaller
the uncertainty in position, the more narrow the peak.
To help you see how waveforms of different
wavelength combine, two such combinations are shown below:
It is apparent that as more waves of
different frequency are mixed, the regions in which they add
constructively diminish in extent. The extreme case would be a wavetrain
in which destructive interference occurs at all locations except one,
resulting in a single pulse:
Is such a wave possible, and if so, what is
its wavelength? Such a wave is possible, but only as the sum
(interference) of other waves whose wavelengths are all slightly
different. Each component wave possesses its own energy (momentum), and
adds that value to the range of momenta carried by the particle, thus
increasing the uncertainty p.
In the extreme case of a quantum particle whose location is known exactly,
the probability wavelet would have zero width which could be achieved only
by combining waves of all wavelengths-- an infinite number of wavelengths,
and thus an infinite range of momentum dp and thus kinetic energy.
Q16. Are they particles or are they waves?
Suppose we direct a beam of photons (or
electrons; the experiment works with both) toward a piece of metal having
a narrow opening. On the other side there are two more openings, or slits.
Finally the particles impinge on a photographic plate or some other
recording device. Taking into account their wavelike character, we would
expect the probability waves to produce an interference pattern of the
kind that is well known for sound and light waves, and this is exactly
what is observed; the plate records a series of alternating dark and light
bands, thus demonstrating beyond doubt that electrons and light have the
character of waves.
Now let us reduce the intensity of the
light so that only one photon at a time passes through the apparatus (it
is experimentally possible to count single photons, so this is a practical
experiment). Each photon passes through the first slit, and then through
one or the other of the second set of slits, eventually striking the
photographic film where it creates a tiny dot. If we develop the film
after a sufficient number of photons have passed through, we find the very
same interference pattern we obtained previously.
There is something strange here. Each
photon, acting as a particle, must pass through one or the other of the
pair of slits, so we would expect to get only two groups of spots on the
film, each opposite one of the two slits. Instead, it appears that the
each particle, on passing through one slit, "knows" about the
other, and adjusts its final trajectory so as to build up a wavelike
It gets even stranger: suppose that we set
up a detector to determine which slit a photon is heading for, and then
block off the other slit with a shutter. We find that the photon sails
straight through the open slit and onto the film without trying to create
any kind of an interference pattern. Apparently, any attempt to observe
the photon as a discrete particle causes it to behave like one.
The only conclusion possible is that
quantum particles have no well defined paths; each photon (or electron)
seems to have an infinity of paths which thread their way through space,
seeking out and collecting information about all possible routes, and then
adjusting its behavior so that its final trajectory, when combined with
that of others, produces the same overall effect that we would see from a
train of waves of wavelength = h/mv.