Go Home
Email: 97005423@lambton.on.ca
It was Einstein’s work that paved the way for all of them for understanding how electrons are arranged in an atom. Plank helped with this theory and eventually Bohr, de Broglie and Heisenburg would all develop their own theories about it and extend them farther to include such things as wave properties of electrons, principal quantum numbers, orbitals, uncertainty principles and quantum mechanics.
Max Planck
Max Karl Ernst Ludwig Planck was born on April 23 1858. In 1874, at the age of 16, he entered the University of Munich. Before he began his studies he discussed the prospects of research in physics with Philipp von Jolly, the professor of physics there, and was told that physics was essentially a complete
science with little prospect of further developments. Fortunately Planck decided to study physics despite the bleak future for research that was presented to him.
In 1878 he received his Doctoral degree the age of 21. In 1889 Planck received an appointment to the university of Berlin. In 1892 he was promoted to ordentlicher professor (full professor). During his life he made many important contributions to the world of theoretical physics, but the one that he will most be remembered for was his quantum theory that he discovered when he was 42 years old and for which he would win the Nobel prize for in 1918.
When an object is heated, the colour of the wavelength of light that is emitted is an indication of the temperature of the object. In the late 1800’s the known laws of physics did not explain this sufficiently.
Then in 1900 Max Planck made the observation that atoms can either release or absorb energy in small fixed amounts. These known bundles of energy Planck called quantum.
He then proposed that the energy released by a single quantum is equal
to the frequency of the light multiplied by a constant.
E=hv
E= energy of a single quantum
H= Planck’s Constant or 6.63*10^-34 joule-seconds
v= frequency
The energy is always absorbed or released in integer multiples of hv. Their energy is always restricted to known values. At first the theory met resistance but due to the successful work of Niels Bohr in 1913, calculating positions of spectral lines using the theory, it became generally accepted.
Planck made no other significant discoveries of comparable importance to his 1900 work but remained a vital figure within the scientific community. He contributed to various branches of optics, thermodynamics and statistical mechanics, physical chemistry, and other fields. He was also the first prominent physicist to endorse Einstein's special theory of relativity. Planck became permanent secretary of the mathematics and physics sections of the Prussian Academy of Sciences in 1912 and held that position until 1938. He also served as president of the Kaiser Wilhelm Society (now the Max Planck Society) from 1930 to 1937. In 1909, his first wife Marie Merck died, leaving Planck with two sons and twin daughters. The elder son, Karl, was killed in action in 1916. The following year, Margarete, one of his daughters, died in childbirth, and in 1919 the same fate befell Emma, his other daughter. The younger son, Erwin, was implicated in the attempt made on Adolph Hitler's life on July 20, 1944, and in early 1945 the Gestapo killed him. At war's end, Planck and his second wife, Marga von Hoesslin, moved to Göttingen. There, on October 4, 1947, in his 89th year, he died.
Niels Bohr
Neils Bohr, having worked with Rutherford on the planetary system of an atom, calculated that the emission of electromagnetic waves would cause the electrons of an atomic system to lose their energy and fall into the nucleus within a fraction of a second. He concluded that Rutherford’s planetary system of electrons revolving around the nucleus could not last for any length of time. This model contradicted the fact that electrons exist permanently. Bohr stated, " Since nature cannot be wrong, conventional mechanics must be wrong, at least when applied to the motion of electrons within an atom."(qtd. In Gamow, 1965, p.314). It was easy for Bohr to criticize Rutherford’s model; Bohr was left with many unanswered questions.
Bohr started with the idea that electrons move in a circular orbit around the nucleus (Rutherford’s model), but as earlier calculations proved, the electron would continuously lose energy by emitting electromagnetic radiation and spiral into the nucleus. By the use of Planck’s idea that energies are quantized, he was able to propose that "only orbits of certain radii, corresponding to certain definite energies, are permitted."(Brown, LeMay & Bursten. 1997, p.191). An electron in an "allowed" (p.191) energy state is in a permitted orbit and has a specific energy; therefore, the electron will not radiate energy and fall into the nucleus. By combining both these ideas, he was able to publish his postulates in 1913. These allowed orbits had a specific energy given by the formula:
En=(-RH)(1/n2) n=principal quantum number
RH= Rydberg constant
In the mid-1800s, scientists first discovered the line spectrum of hydrogen. Johann Balmer came up with a simplistic formula for this line spectrum given by:
n = C(1/22 – 1/n2) n=3, 4, 5, 6
n = frequency
C= a constant (3.29x10-15 s-1)
The simplicity of Balmer’s equation could not be explained at that time.
This equation did work, but where did this constant come from and what
exactly was n? Thirty years later, Bohr was able to explain the line spectrum
of hydrogen. By combining the Plank-Einstein hypothesis (E=hn
) and Balmer’s simple formula, he was able to come up with an equation
he used to explain the relationship between the frequency of absorbed or
emitted light and the principal quantum number of the two states. The constant
of the Balmer’s equation was in fact RH/h. This equation is given by:
nf= final state
RH= Rydberg constant (2.18x10-18 J)
h= Planck’s constant (6.63x10-34 J-s)
n = frequency
Bohr explained the line spectrum of the hydrogen atom by assuming that electrons can jump from one energy state to another by absorbing or emitting photons of radiant energy. Radiant energy is emitted when an electron jumps to a lower energy level and absorbed when it jumps to a higher energy level. The wavelength of the frequencies could then be calculated by l = c/n .
"The criterion for the validity of any new theory in physics is not only that this theory should give a correct interpretation of the previous observations, but that it also predict things that can later be confirmed by direct experiment."(Gamow, 1965, p. 316). Bohr’s theory fit this criterion because it not only interpreted Balmer’s formula, it also predicted the spectral lines when an electron jumps from the higher orbits to the first or third orbit in the hydrogen atom. The spectral lines when an electron jumps from a higher orbit to n=1 were expected to be found in the ultraviolet region, and were found by Lyman (an English spectroscopist). The spectral lines corresponding to electrons jumping to n=3 were expected to be found in the infrared region, and were found by Paschen (a German spectroscopist). The major problem with Bohr’s theory is that it was limited; he could only explain atoms and ions with a single electron
de Broglie.
After Bohr completed his theory about the hydrogen electron, the question everyone was asking was why are the energies of the hydrogen electron quantized? For years no one had figures it out. But in 1924, physicist Louis de Broglie found a solution to the question.
His reasoning was that if light waves can behave like a stream of particles, called photons, the maybe particles such as electrons can posses wave properties. According to him the electrons that are bound to the nucleus behave like standing waves. An example of this would be like a guitar string that has been plucked. At the ends of the string there are nodes where there is no movement at all. The greater the frequency of the vibration the shorter the wavelength and the greater the number of nodes.
DeBroglie also said the if an electron behaves like a standing wave the length of the wave must fit the circumference of the orbit or else the wave partially will cancel itself out on each orbit and eventually the amplitude of the wave would be reduced to zero. So then the wave would not exist.
The equation given for the relationship between the circumference of the orbit and the wavelength is
2p r = nl
Where r - radius of orbit
l - Wavelength of electron
n - 1, 2, 3,…..
Because n is always a whole number that means that r can only have certain values as n increases. And since the energy of the electron depends on the size of the orbit (r) its value must be quantized.
DeBroglie concluded that the waves can behave like particles and that particles can exhibit wave properties.
Particles and wave properties are related by
l = ____h_____
mv
Where l - wavelength
m - mass
v - velocity
h - Planks constant = 6.63* 10^-3 J-s
This equation shows that a particle in motion can be treated as a wave and a wave can exhibit the properties of a particle.
Because de Broglies theory can be used for all matter, any object with a certain mass and velocity would give rise to a characteristic matter wave.
Realistically, an object of ordinary size, like a ping pong ball, its mass is too big to actually observe any wavelength, but for a electron its much easier to observe because its mass is so small.
A few years after de Broglie published his theory, Clinton Davisson and Lester Germer in the U.S. and G.P. Thomasson in England showed that electrons do have wavelike properties. They now use this idea for electron diffraction in electron microscopes. It uses the wavelengths of electrons to produce pictures of objects too tiny to see with the naked eye.
Another few years later in 1929 de Broglie received the Nobel Prize in physics for his wave - particle theory.
Heisenburg
Werner Heisenberg was born December 5, 1901, in Wurzburg, Germany. He studied theoretical physics at the University of Munich, and completed his doctoral dissertation in 1923. He then studied under Max Born in Gottingen and in the fall of 1924, under Niels Bohr in Copenhagen, Denmark. From 1927 through 1941, Heisenberg was a professor of theoretical physics at the University of Leipzig. Heisenberg developed a purely mathematical model of the atom and used matrix mechanics to explain the wavelengths of spectral lines. Heisenberg also wrote many philosophical works. During World War II, he worked at the Kaiser Wilhelm Institute of Physics in Berlin with Otto Hahn to develop a nuclear reactor. His best known accomplishment was his paper on the Uncertainty Principle.
Heisenberg’s Uncertainty Principle was written in 1927 and for his efforts in 1932 he received the Nobel Prize. It said the process of measuring the position x of a particle will disturb the particle's momentum p, so that Dx Dp = h, where Dx is the uncertainty of the position, Dp is the uncertainty of the momentum, and h is Planck's constant. Heisenberg's work was based on matrix mathematics used by Cayley on matrices 50 years earlier.
The uncertainty principle was not welcomed by everyone. One of its greatest
opponents was Albert Einstein. He created a hypothetical situation (thought
experiment) to challenge Niels Bohr at a conference they attended in 1930.
Einstein’s experiment was this:
A box was filled with radiation and a clock. The clock was outfitted
with a shutter designed to allow only one photon of light to escape the
box. After the photon was allowed to escape the box the box was then weighed.
This would allow both the time and the energy of the photon to be measured.
Niels Bohr spent the night trying to find a solution. The next morning he triumphed. His solution was that the mass is measured by hanging a weight under the box, this weight will in turn give some momentum to the box and thus cause small error in measuring the position. Einstein, according to his theory on relativity, had said time was not absolute and therefore an error in the measurement of box’s position would also cause an error in the measurement of the time, a la Einstein’s own thought experiment. [JOC/EFR]
The mathematical proof of the Uncertainty Principle is as follows:
If we use light, in this case a single photon to minimize the amount
of interaction, of the wavelength l to examine
the position of the particle then the uncertainty Dx
in the measurement is approximately equal to:
Dx = h
A small amount of interference will be caused by the impact of the photon
and slightly change the momentum by the amount h/l:
Dp = h/l
The product of the two uncertainties is
DxDp = h
Using the same experiment we can attempt to measure the energy of a
particle. Again we use a single photon with wavelength l.
The time in which the particle is measured will be uncertain by the amount
l hence:
Dt = l/c
where c is the velocity of the photon.
Photons have an initial energy of hc/l of
which some small portion is transferred to the observed particle. Therefore
the uncertainty of the test particle after interaction with the single
photon is:
DE = hc/l
The product of the two uncertainties yeilds
DEDt = h
[Shull, Snow]
The Contributions of these four men paved the way to explain the trends
in the periodic table and to understand chemical reactivity. This helped
in developing electron microscopes, hydrogen bombs, laser technology and
to understand magnetic fields which also helped in better understanding
chemistry and medicine. Without the theories of these men we may have never
developed something like the X ray machine. So yes these theories and ideas
may be boring to us, but without them our world may not be as quite as
advanced as we are now. Imagine a world without CD players! What would
you do?
LITERATURE CITED
Gamow, G. (1965). Matter, Earth and Sky. (2nd Edition).
New Jersey: Prentice-Hall, Inc.
Brown, T.L., LeMay, H.E., Bursten, B.E. (1997) Chemistry: The Central
Science. (7th Edition). USA: Prentice-Hall, Inc.
Close M., The Uncertainty Principle Begins. Online. http://www.honors.unr.edu/~fenimore/wt202/close/#principle
JOC/EFR 1996 Quantum Age Begins. Online. http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/The_Quantum_age_begins.html#54
Shull, J. Michael, Snow, Theodore P. (1986) Physics.USA West
Publishing
Browns, Bursten, Lemay, (1997) Chemistry. The Central Science
(7 edition) PreticeHall(1997)
http:www.chembio.uogulph.ca/educmat/chm386/rediment/tourguan/broglie.htm