Quantum Mechanics
Planck’s Law  Photoelectric Effect  Bohr Atom  De Broglie Wavelength  Heisenberg’s Uncertainty Principle  The Schrdinger equation  Relativistic Effects: element 137  Solvay Conferences
Planck’s Law
The word quantum derives from the Latin, meaning “how much” or “how great”. Planck’s hypothesized that energy is radiated and absorbed in discrete “quanta” or energy packets which aligned well with observed patterns of blackbody radiation. 
In 1900, Planck proposed a relationship, which later became known as Planck’s Law which states every quantum of a wave has a discrete amount of energy given by Planck’s equation: 
E=h 
with 
E = energy, 
h = Plank’s constant (6.62607 x 1034 J s), 
= frequency 
Planck considered his quantum hypothesis a mathematical trick to get the right answer rather than a sizable discovery. Max Planck is won the 1921 Nobel Prize in Physics for this work. 
Many others contributed to the development of Quantum Mechanical theory, especially in the first half of the 20th century. Some prominent contributors were: 
Albert Einstein 
Arnold Sommerfeld 
Arthur Compton 
Enrico Fermi 
Erwin Schrdinger 
Louis de Broglie 
Max Born 
Niels Bohr 
Paul Dirac 
Satyendra Nath Bose 
Werner Heisenberg 
Wilhelm Wien 
Wolfgang Pauli 
Photoelectric Effect
In 1887, Heinrich Hertz observed that electrodes illuminated with ultraviolet light could cause an electrical discharge (sparks).

In 1902, Hungarian physicist Philipp Lenard showed the ionization of gases by ultraviolet light, producing positive and negative ions. Lenard observed that the energy of individual emitted electrons increased with the frequency of the light. This appeared to be contradict Maxwell’s wave theory of light, which predicted that the electron energy would be proportional to the intensity of the radiation. Lenard did not offer an explanation for the observation.

Experimentation showed that: 
The intensity of the light source had no effect on the maximum kinetic energy of the electrons. 
Below a certain frequency, the photoelectric effect does not occur at all. 
There is no significant delay between the light source activation and the emission of the first electrons. 
In 1905, Albert Einstein published a paper, “On a Heuristic Viewpoint Concerning the Production and Transformation of Light”. This paper proposed the simple description of “light quanta”, now called photons. 
Einstein explained the results of Lenard’s experiment by describing light as discrete quanta, rather than continuous waves. This interpretation was based on Max Planck’s theory of blackbody radiation published a few years earlier (1900). 
In 1914, Robert Millikan’s confirmed Einstein’s explanation of the photoelectric effect. Einstein was awarded the Nobel Prize in 1921 for “his discovery of the law of the photoelectric effect”, and Millikan was awarded the Nobel Prize in 1923 for “his work on the elementary charge of electricity and on the photoelectric effect”.

Plank’s Law 
E=h 
with 
E = energy, 
h = Plank’s constant (6.62607 x 1034 J s), 
= frequency 
The Bohr Atom
Neils Bohr founded the Institute of Theoretical Physics at the , now known as the , in 1920. He predicted the existence of a new like element, which was named , after the Latin name for Copenhagen, where it was discovered. Later, the element Bohrium was named after him. 
In September 1943, word reached Bohr that he was about to be arrested by the Germans, and he fled to Sweden. From there, he was flown to 
Bohr proposed the atomic model in 1913 according to which the electrons travel in circular orbits around the nucleus due to electrostatic force. It was actually the modification of Rutherford’s atomic model who predicted electronic cloud around a positively charged nucleus. Rutherford’s model however faced some technical difficulties when viewed in terms of classical mechanics. This model did not use orbits of fixed positions. The model was defective because according to classical mechanics the orbiting electron will lose energy and ultimately fall into nucleus. Also as the orbit will get smaller and smaller the frequency of the emitted radiation will increase, which is not seen in emission spectra. Such a model of an atom was not acceptable since it shows that all atoms are unstable which is not applicable. 
Bohrs atomic model was also based on the classical mechanics but a quantum concept was introduced into it by stating that the electrons can revolve around the nucleus only in certain allowed circular paths. He postulated that: 



Bohrs model was based upon Planck’s quantum theory of radiation introduced by Max Planck in 1900 which stated that energy can only be emitted or absorbed in discrete amounts. 
The energy difference between the electronic orbits can be found by using Planks Law equation which is: 
E = E2 – E1 = h 
Where h is Plancks’s constant and is the frequency of radiation emitted. According to the postulate 3 the laws of classical mechanics were valid for the motion of electrons only when viewed in terms of quantum rule i.e. the electrons can only radiate a certain discrete amount of energy by jumping from one orbit to another. Thus the energy of the electron in an orbit is fixed and so is angular momentum. The angular momentum is an integral multiple of fixed unit given by: 
L = n h/2 = n 
Where = h/2 and n = 1, 2, 3…is a principal quantum number and its lowest value is 1. Bohr model was successfully applied to calculate the orbital energies of hydrogen and hydrogen like atoms. 
Electrons energy level of hydrogen atom

Bohr model provided the expression for calculating the energy level of hydrogen atom (and hydrogen like atoms) by considering two concepts, the classical and quantum concept. The first is the classical mechanical concept that electrons revolve in circular orbit due to electrostatic force and centripetal force is equal to the Coulomb force: 
Where me is the mass of electron, assumed to be much less than the nuclear mass. Rearranging the above equation provided the speed of electrons: 
The total energy of electron at any radius is given by: 
The negative total energy suggests that it require energy to take electron out of the orbit away from proton. Now according to the quantum rule, the angular momentum is an integral multiple of n: 
mevr = n 
Putting the value of velocity and rearranging this equation would give the value of radius of nth orbit of an atom: 
For n=1 the smallest radius of hydrogen atom can be found (Z=1 for hydrogen) and its value comes out to be 5.29 * 1011 m. Similarly the Bohrs model enabled the calculation of energy of nth orbit by putting the expression of rn in the energy expression. 
Bohrs model was an important step to understand the absorption and emission spectra of atoms which contained discrete lines. Bohr model related these discrete lines in the atomic spectra to the difference in the electronic orbits in atoms. However this was not achieved by Bohr himself because the idea that the electrons can behave as material waves was suggested eleven years later but still the Bohrs concept of discrete energy levels was a significant step in understanding the electrons behavior in atom and towards the development of quantum mechanics. 
De Broglie Wavelength
One of the persons to extend Planck’s work was Louis de Broglie. In 1924 De Broglie, in his PhD thesis, proposed that electrons would also exhibit wavelike properties similar to light. De Broglies logic was based on two fundamental principles of physics. 
The first was Einsten’s famous equation E=mc^{2}, generally associated the “Theory of Relativity” and also extended from Newtons expression of kinetic energy (E=mv^{2}). 
E=mc^{2} 
With 
E = energy, 
m = mass, 
m = speed of light 
The second equation was Planck’s Law which states every quantum of a wave has a discrete amount of energy given by Planck’s equation: 
E=h 
with 
E = energy, 
h = Plank’s constant (6.62607 x 1034 J s), 
= frequency 
De Broglie hypothesized that the two energies would be equal. 
mc^{2}=h 
Or for particles not traveling at the speed of light; 
mv^{2}=h 
And since the speed of light C, is constant and defined by relationships of frequency () and wavelength (). (c=v) 
Then various mathematical rearrangements Produce. 
mv^{2}=hv=c/v 
Hence: 
=hvmv^{2}=hmv 
The association of wavelength with mass was not proven by de Broglie in his thesis, but was proven in several scientific experiments a few years later. This work was fundamental in supporting the principle of waveparticle duality, first described by Einstein in 1905, which is a fundamental principle of modern quantum mechanics. DeBroglie’s contribution was to associate a wavelength with any mass. As a matter of realworld connection, this work also inspires and explains the principle of an electron microscope, common in the modern scientific world. 
Heisenberg’s Uncertainty Principle
Heisenberg’s uncertainty principle, also known as the uncertainty principle, was first introduced in 1927, by the German physicist Werner Heisenberg. Heisenberg believed that the more precisely the position of some particle is determined, the less precisely its momentum can be known, and vice versa. Specifically Heisenberg was referring to the complementary variables, position x and momentum p.
Heisenberg’s uncertainty principle, also known as the uncertainty principle, was first introduced in 1927, by the German physicist Werner Heisenberg. Heisenberg believed that the more precisely the position of some particle is determined, the less precisely its momentum can be known, and vice versa. Specifically Heisenberg was referring to the complementary variables, position x and momentum p.
(In this equation hbar is the reduced Planck’s constant and Sigma is the standard deviation of the measurements x and p.)
Often the Uncertainty Principle is confused with another similar effect in physics, called the “observer effect”. The observer effect notes that measurements of certain systems cannot be made without affecting the systems themselves. An example of this is trying to measure the length of a rubber band without stretching the rubber and thereby introducing an error into the length measurement.
It is now understood that the uncertainty principle is inherent in the properties of all wavelike systems, which is a fundamental principle of quantum mechanics. Thus it is now understood the the uncertainty principle was not a function of measurement uncertainty, but actually a function of the matterwave property of quantum objects.
To simplify the understanding of this discussion it may help to think of the path of Earth around the Sun. In this case Earth is held in its orbit by two forces, 1) gravity due to the sun and the other planets, and 2) velocity or angular momentum. In this case, Newton’s Laws of Motion apply. The path of electrons about the nucleus is similar except that the forces are different. However the fundamental difference in this analogy is the electrons are not traveling in straight line circlelike orbits. Instead they are traveling in wave form. In this case classical mechanics (Newton’s Laws of Motion) is replaced by modern Quantum Mechanical theory.
The Schrdinger equation
Early assumptions of quantum mechanics was that energy had to be “quantized” which means that electrons had to exist in discrete energy levels. This was a fundamental principle of the Bohr atom. It was also observed that subatomic particles, such as electrons, travel in wavelike form, similar to light. This was realized when it was observed that electrons, when passed through a double slit, behaved similar to light.
There was a great deal of work by the leading physicists of the day to develop the math that would accurately define this new theory. Schrodinger was the first person to develop just such a wave equation. Once written, there was a great deal of discussion as to just what the equation meant. This topic requires an understanding of high level mathematics beyond the scope of this project. Suffice to say, the best test of the equation was when it was used to solve for the energy levels of the Hydrogen atom, and the energy levels were found to be in accord with Rydberg’s Law.
Relativistic Effects: element 137
Quantum Mechanics has been successful at producing the math that accurately supports and predicts the outcomes of observation and experimentation. One relationship is understanding the effects of energy levels and the velocity of electrons needed to travel the orbits at these energy levels. For example it is known and calculated that the speed of electrons must increase as n orbital increase. This is particularly true for the 1s electrons. As n levels increase, the velocity of electrons approaches the speed of light, which is regarded in modern physics as maximum velocity. There it can be predicted that the ultimate atomic number can only increase to a certain maximum number.
In the Bohr Model, an n = 1 electron has a velocity given by
, where Z is the atomic number, alpha is the finestructure constant, and c is the speed of light. In nonrelativistic quantum mechanics, therefore, any atom with an atomic number greater than 137 would require its 1s electrons to be traveling faster than the speed of light. The significance of element 137, also known as untriseptium, was first pointed out by the physicist Richard Feynman. Element 137 is sometimes informally called feynmanium (symbol Fy). However, Feynman’s approximation is challenged by other physicists whose calculations suggest that elements up to element 173 are possible.
Solvay Conference
First Conference
The first Solvay Conference, 1911, was an invitationonly meeting sponsored by Belgium industrialist Ernest Solvay. Thje purpose was to bring together the greatest physicists of the day. The conference was considered a turning point in modern physics. Due to the success of the conference , The International Solvay Institutes for Physics and Chemistry, was founded a year later (1912) in in Brussels, Belgium Hendrik A. Lorentz was chairman of the first Solvay Conference held in Brussels in the autumn of 1911. The subject was Radiation and the Quanta. This conference looked at the problems of having two approaches, namely the classical physics and quantum theory.
Photograph of the first conference in 1911 at the Hotel Metropole. Seated (LR): W. Nernst, M. Brillouin, E. Solvay, H. Lorentz, E. Warburg, J. Perrin, W. Wien, M. SklodowskaCurie, and H. Poincare’. Standing (LR): R. Goldschmidt, M. Planck, H. Rubens, A.
Fifth Conference
Perhaps the most famous conference was the October 1927 Fifth Solvay International Conference on Electrons and Photons, where the world’s most notable physicists met to discuss the newly formulated quantum theory.
This conference was also the culmination of the struggle between Einstein and the scientific realists, who wanted strict rules of scientific method as laid out by Charles Peirce and Karl Popper, versus Bohr and the instrumentalists, who wanted looser rule.
The individual success of these participants is phenomenal, 17 of the 29 attendees were or became Nobel Prize winners, including Marie Curie, who alone among them, had won Nobel Prizes in two separate scientific disciplines (Chemistry and Physics).
Fifth conference participants, 1927. Institut International de Physique Solvay in Leopold Park.
First row
: I. Langmuir, M. Planck, M. SklodowskaCurie, H.A. Lorentz, A. Einstein, P. Langevin, Ch.E. Guye, C.T.R. Wilson, O.W. Richardson.
Second row: P. Debye, M. Knudsen, W.L. Bragg, H.A. Kramers, P.A.M. Dirac, A.H. Compton, L. de Broglie, M. Born, N. Bohr.
Third row: A. Piccard, E. Henriot, P. Ehrenfest, E. Herzen, Th. de Donder, E. Schrdinger, J.E. Verschaffelt, W. Pauli, W. Heisenberg, R.H. Fowler, L. Brillouin.
Solvay Conferences on Physics
No. 
Year 
Title 
Translation 
Chair 
1 
1911 
La thorie du rayonnement et les quanta 
The theory of radiation and quanta 
Hendrik Lorentz (Leiden) 
2 
1913 
La structure de la matiLa thre 
The structure of matter 
Lorentz 
3 
1921 
Atomes et La thlectrons 
Atoms and electrons 
Lorentz 
4 
1924 
ConductibilitLa th La thlectrique des mLa thtaux et problLa thmes connexes 
Electric conductivity of metals and related problems 
Lorentz 
5 
1927 
Electrons et photons 
Electrons and photons 
Lorentz 
6 
1930 
Le magnLa thtisme 
Magnetism 
Paul Langevin (Paris) 
7 
1933 
Structure et propriLa thtLa ths des noyaux atomiques 
Structure & properties of the atomic nucleus 
Langevin 
8 
1948 
Les particules La thlLa thmentaires 
Elementary particles 
William Lawrence Bragg (Cambridge) 
9 
1951 
L’La thtat solide 
The solid state 
Bragg 
10 
1954 
Les La thlectrons dans les mLa thtaux 
Electrons in metals 
Bragg 
11 
1958 
La structure et l’La thvolution de l’univers 
The structure and evolution of the universe 
Bragg 
12 
1961 
La thLa thorie quantique des champs 
Quantum field theory 
Bragg 
13 
1964 
The Structure and Evolution of Galaxies 
J. Robert Oppenheimer (Princeton) 

14 
1967 
Fundamental Problems in Elementary Particle Physics 
Christian Mller (Copenhagen) 

15 
1970 
Symmetry Properties of Nuclei 
Edoardo Amaldi (Rome) 

16 
1973 
Astrophysics and Gravitation 
Amaldi 

17 
1978 
Order and Fluctuations in Equilibrium and Nonequilibrium Statistical Mechanics 
Lon van Hove (CERN) 

18 
1984 
Higher Energy Physics 
vanHove 

19 
1987 
F. W. de Wette (Austin) 

20 
1991 
Paul Mandel (Brussels) 

21 
1998 
Dynamical Systems and Irreversibility 
Ioannis Antoniou (Brussels) 

22 
2001 
The Physics of Communication 
Antoniou 

23 
2005 
The Quantum Structure of Space and Time 
David Gross (Santa Barbara) 

24 
2008 
Quantum Theory of Condensed Matter 
Bertrand Halperin (Harvard) 

25 
2011 
The theory of the quantum world 
David Gross 

26 
2014 
Astrophysics and Cosmology 
Roger Blandford (Stanford) 