Niels Bohr and Quantum Theory
Birth and early years (1885-1903)
Niels Bohr was born in Copenhagen on 7 October 1885. His father was a Professor of Anatomy in Copenhagen University. His mother Ellen was a jew. The family had bankers and politicians.
​
Niels grew up with his elder sister Jenny and brother Harald who was 18 months younger than him. The family was very progressive in its views. Niels and
Harald were educated in the highly respected Gammelbohm gymnasium. Harald was better than Niels in studies and was very good in sports. He was particularly good in Mathematics and football.
​
Although there was rivalry between the brothers there was no enmity. Harald was interested in Mathematics while Niels was interested in Physics. So they
helped each other. Jenny was educated in Copenhagen University and later in Oxford University. She returned to Denmark and was a very good teacher, but
she became ill and died.
​
Copenhagen University (1903-1911)
In 1903, both Niels and Harald joined Copenhagen University. Both became good foot-ballers. Niels was goal-keeper; he will be working out Mathematics problems when the ball was on the other side. Harald was in the Denmark team and won over France in the Olympic games.
​
Students called both the brothers as genius. Niels was much interested in reading books. He already knew about the new discoveries in Physics. He used to find out the mistakes in books. His father often invited intellectuals for dinner at home. After dinner there was interesting conversation. The brothers were allowed to listen quietly. This may be the reason for Bohr's enthusiasm for philosophical debates in later days.
​
In 1907, at the end of his degree education, Niels Bohr won the gold medal of the Royal Danish Academy. This was for his research dissertation. His research
was on surface tension. He included the results of his experiments in the dissertation. He succeeded in measuring the frequency of vibration of water jets of radius less than a millimetre.
​
He started his research for his doctorate in 1909. It was on the electron theory of metals. In 1897 JJ Thomson discovered the electron. He found that electron was negatively charged and its mass was about a thousand times lower than the mass of the lightest atom which was Hydrogen. He had proposed that the positive charge of the atom was spread throughout its volume while the electrons were embedded at various points. This was called the plum-pudding model.
​
It was supposed that in a metal some of the electrons escaped from the atoms and were freely moving. This was called the electron theory of metals. Bohr's
thesis was a criticism of this theory. He analyzed the shortcomings of the electron theory of metals. He received the doctorate in 1911.
​
Cavendish Laboratory (1911)
In 1911, Bohr got the Carlberg scholarship for study abroad and went to Cavendish laboratory in Cambridge to pursue research with JJ Thomson.
​
But at Cambridge he was disappointed. Thomson did not have time to work with young researchers. Further since Bohr's English was not good, conversation
between him and Thomson was difficult. Thomson did not have the patience to understand Bohr.
​
Bohr also had much to learn. Just as he was finding the mistakes in books in his younger days, he now was finding mistakes in Thomson's research papers.
Thomson did not like it. Bohr wanted to go elsewhere, but he liked England. So he decided to learn English well. With the help of a Dutch-English dictionary
he started reading the novels of Charles Dickens.
​
In October, Ernest Rutherford gave a lecture at Cavendish. Because of this lecture and the discussions that took place after the lecture, Niels Bohr developed great respect towards Rutherford. Rutherford also formed a good opinion about Bohr from their mutual conversation. He said: " This guy is the brightest among those I saw."
​
Rutherford was the Head of the Physics Department of Manchester University. As a consequence of his discovery of the atomic nucleus, the model of the atom changed from Thomson's model. Rutherford changed it to the solar system model. Just as the planets orbit the Sun, electrons orbit the nucleus, in Rutherford's model. Most of the mass of the atom was in the nucleus. But there was an important defect in Rutherford's model. In classical physics, the orbiting electrons will
lose their energy by radiation of electromagnetic waves and fall into the nucleus in about second. So atom will not be stable.
​
Manchester University (1911-1912)
Rutherford invited Bohr to come to Manchester. Since Bohr did not like Cambridge, he accepted that invitation and went to Manchester.
​
Bohr told Rutherford that he is going to work on the puzzle why the electron does not fall into the nucleus. Rutherford said it is a difficult question, but he had
high opinion about Bohr's capability and so let him work on it. Bohr began to study why the electrons orbit the nucleus without losing their energy.
From 1850, spectroscopy became a well-established subject. But since it was taught as a part of Chemistry not taught in Physics, Bohr did not know much
about it. It was known that every element emitted light of a characteristic colour when heated. The spectral lines with well-defined frequencies helped to identify
the element. The spectral lines from the Sun led to the discovery of the element Helium.
​
Bohr surmised that the spectral lines from each element contain the secrets of the atomic structure. So he began to study spectroscopy. The best known spectrum
was the spectrum of Hydrogen. In 1885, Johann Balmer had discovered a formula for the frequencies of the Hydrogen spectrum, which agreed with the measured frequencies very well. But nobody knew the origin for Balmer's formula.
​
It is here that Bohr's innovation came out. He played with Balmer's formula for a while and found that the formula can be written in a different way.
​
In 1900, Planck had discovered that radiation from a heated body (called black body) were made of quantized packets. Energy of a quantum E was related to the
frequency of the wave by the formula:
where h is called Planck's constant. Using this idea of the quantum, in 1905, Einstein succeeded in explaining the laws of photoelectric effect.
​
Bohr realized that there is a connection between the Hydrogen spectrum and the quantum theory of Planck and Einstein. He further surmised that the orbits of
the electron in the atom are quantized, or rather the orbital angular momentum of the electron is quantized. He discovered the formula for the quantization of
the orbital angular momentum l:
​
​
Bohrs's hypothesis is that only those orbits with these quantized orbital angular momentum are allowed for the electron and while the electron is in this allowed orbit, it does not radiate electromagnetic wave.
​
When the electron jumps from one allowed orbit to a lower orbit with lower energy, the difference of energy is emitted as a quantum with energy E given by the Planck's formula above. When the electron is in the lowest allowed orbit, it is in the ground state and it becomes stable.
​
From these ideas, Bohr succeeded in theoretically deriving the empirical Balmer formula. This is the Bohr model of the atom.
​
Copenhagen University (1912-1914)
In the summer of 1912 Bohr returned from Manchester to Copenhagen. There he married Margarethe Nordund whom he had met one year earlier. He joined as a lecturer in Copenhagen University. But he continued to have connection with Manchester and was communicating his ideas with Rutherford.
​
Bohr began to write the research paper on his allowed electron orbits. But he generally took long time to finalize any writing. He wrote and rewrote the paper many times. Rutherford lost patience.
​
In March 1913, Bohr sent his final version to Rutherford. Rutherford did not like one part of it and asked Bohr to remove it. Immediately Bohr went to Manchester and argued with Rutherford night and day. He did not agree to leave out even one line from his paper. Finally, Rutherford had to accept defeat. Bohr's paper was published in the Philosophical Magazine and shook the world of Physics.
​
All of a sudden, everybody began to discuss Bohr's theory of the atom. They did not like it. Even the quantum theory of Planck and Einstein was not liked by most scientists. The famous scientist Max von Lae said the he will leave Physics if Bohr's theory is proved right.
​
The reason for the opposition to Bohr's theory was because it was a mixture of classical physics and quantum physics. Angular momentum belonged to classical physics while Planck's constant was quantum physics. Bohr's reply was that by combining both, you get the correct frequencies of the Hydrogen spectrum and also you get Balmer's formula.
​
However, a difficulty surfaced. Experimentally, inside each spectral line many spectral lines were found to be present. There was no explanation for this multiplet structure of spectral lines in Bohr's theory.
​
The famous theoretical physicist Arnold Sommerfeld who was a great supporter of quantum theory realized that electrons had elliptical orbits also apart from the circular orbits that Bohr had used. In addition he could make Bohr's theory relativistic. This improved theory of Sommerfeld gave the multiplet structure of the spectral lines correctly.
​
Nevertheless, most scientists still opposed Bohr's theory. The basic difference between classical physics and quantum physics appeared irreconcilable.
​
Another difficulty was that Bohr's theory of Hydrogen atom could not be extended to other atoms. Bohr tried very hard, but did not succeed.
​
In Copenhagen University Bohr had to spend much time lecturing to students which he could not manage. So, in 1914, when Rutherford invited him to join Manchester University as a researcher, he immediately accepted it. There he did not have to lecture.
​
Manchester (1914-1916)
World War I started even before Bohr went to Manchester. He and his wife had to undergo much difficulty in going round the coast of Scotland, to reach Manchester.
​
Even during the war, news from Germany came to Manchester. Using the Bohr-Sommerfeld model, Sommerfeld and others made many discoveries which were subjected to experimental tests. Although many puzzles were still not solved, the model continued to attract many supporters.
Copenhagen (1916-1962)
Bohr's fame spread far and wide. The Denmark Government did not want to lose its citizen who was a genius. It gave Professorship to the 30-year old Bohr. So Bohr and his wife undertook the hazardous journey back to Denmark.
​
The government established an Institute of Theoretical Physics for Bohr. He set it up on the model of Rutherford's laboratory. Soon Bohr's Institute became the Mecca of Theoretical Physics.
​
Those who joined as Professors in Copenhagen University were supposed to go in front of the King and introduce themselves. Bohr went for that with the appropriate dress. The King shook his hands and said he was proud to meet a great foot-baller! Bohr said that was his brother. The King terminated the meeting and Bohr left!
​
In 1918, work started on the construction of the Institute of Theoretical Physics. Although it was called as Institute of Theoretical Physics, it had laboratories too. The famous Beer company Carlberg gave financial support to the Institute. Since the beginning, the Institute attracted great physicists.
​
Structure of the Atom
Bohr succeeded partially in explaining the structure of atoms beyond Hydrogen. Two discoveries were essential for that. One was the spin of the electron discovered by Uhlenbeck and Goudsmit. This intrinsic spin of the electron will be permanently with the electron; its speed can neither be increased nor decreased. The spin can have two directions, from left to right or right to left.
​
The second important discovery was Pauli's Exclusion Principle. Only two electrons with the two directions of spin are allowed to occupy any allowed orbit of Bohr-Sommerfeld. Any allowed orbit with one direction of spin is called a quantum state. In any quantum state, only one electron is allowed. This is Pauli's Exclusion Principle.
​
With the help of these two discoveries, the structure of all the atoms Hydrogen, Helium, Lithium, Beryllium...Uranium began to be understood. Hydrogen has a single electron. Helium has two electrons and both of them with the two spin directions can occupy a single orbit. Lithium has three electrons and so one of the electrons has to occupy a higher orbit. In this way all the atoms upto Uranium with 92 electrons could be built up.
​
Many years earlier, Mendeleev had ordered the known elements according to their chemical properties and prepared his famous Periodic Table Of Elements. The basic reasons for the periodic chemical properties was explained by the Bohr-Sommerfeld theory with electron spin and exclusion principle. The number of electrons contained in the atom was called Atomic Number. Hydrogen's Atomic Number is 1 and the Atomic Number of Uranium is 92.
​
Using this model, Bohr discovered that an element with Atomic Number 72 must be added to the periodic table. Spectroscopic research later confirmed the existence of such a new element. Bohr received the Nobel Prize in 1922 for this prediction.
Bohr model attained many successes. Experiments also supported the model. But in Bohr model classical physics and quantum theory were combined although they were mutually inconsistent. Light quantum (photon) was emitted only when the electron jumped from a higher orbit to a lower one. When it was going in one orbit, no light was emitted. According to classical physics electromagnetic waves must be emitted during electron's motion in one orbit. How can both classical physics and quantum physics function inside the atom at the same time?
​
Bohr maintained this is possible. He discovered that in the limit of high frequencies or high energies, both quantum theory and classical physics agree with each other. This is called Correspondence Principle.
​
In the years 1920-1923, all the great physicists began to do research in quantum theory. For that Bohr's institute became the Centre. World-famous scientists came there - Wolfgang Pauli from Switzerland, Paul Dirac from England, Werner Heisenberg and Erwin Schrodinger from Germany, Lev Landau from Russia and many others.
​
Pauli discussed his Exclusion Principle with Bohr. He came to Copenhagen many times and debated with Bohr for hours. After that Pauli published his paper.
​
Quantum Mechanics
Quantum revolution started through Planck's discovery in 1900 and einstein's discovery in 1905. Bohr used this quantum idea to stabilize the atom.
​
But there were many puzzles. There were many inconsistencies since quantum was introduced into classical physics. Real Quantum Mechanics in which these inconsistencies were absent was born only in 1924. The architects of real Quantum Mechanics were Werner Heisenberg, Erwin Schrodinger and Paul Dirac.
​
Heisenberg pursued an entirely novel path. He eschewed models completely and developed quantum mechanics through the mathematics of matrices. This was not understandable by most physicists.
​
Schrodinger's way was wave mechanics understandable by physicists. In 1923, Luis de Broglie had proposed an entirely new idea. He proposed that all material objects and material particles like electrons had a wave nature. If an electron has a momentum p, the corresponding wave has a wavelength lambda given by
​
where h is Planck's constant. This can be compared to Planck's equation:
​
​
In these equations p and E are properties of particles while are properties of waves. Planck's constant h connects these.
​
Which law determines the dynamics of these waves? Just as the dynamics of particles is determined by Newton's law, the dynamics of waves must be determined by some law. Schrodinger discovered that law. It is called Schrodinger's equation which is a differential equation for Schrodinger's wave (called wave function)
Heisenberg's Matrix Mechanics and Schrodinger's Wave Mechanics were about the same Physics, but they appeared to live in different worlds. Schrodinger himself and then Paul Dirac showed that the two forms of quantum mechanics are related. It was Dirac who discovered the basic principle behind Quantum Mechanics. He showed that Schrodinger's form and Heisenberg's form were two representations of the same Quantum Mechanics and further that there were many other representations also.
​
Heisenberg and Schrodinger came to Copenhagen separately and discussed with Bohr. Many times at the height of the arguments, Bohr and Heisenberg fought. In the same way, the debate between Bohr and Schrodinger ended in a fight. But these fights did not last long.
​
During this time, Heisenberg discovered his famous Uncertainty Principle which states that the position and momentum of a particle cannot be determined accurately.
​
Bohr also discovered a principle, called Complementarity Principle which states that any phenomenon in Physics cannot be described fully. If we describe one half, the other half will disappear. If the wave properties are specified, the particle properties will disappear and vice versa.
​
These principles helped to keep the contradictions in quantum mechanics under control and served to understand quantum mechanics better. Wave-Particle Duality was an important part of this understanding.
​
Heisenberg-Schrodinger-Dirac Quantum Mechanics became a complete theory. Every consequence of quantum mechanics was subjected to experimental tests and verified.
​
Nevertheless, the contradictions in quantum mechanics generated many debates. The following were the things that could not be fully understood.
​
1. Unlike in classical physics, in quantum mechanics, the experimenter and his apparatus played a major role. In classical physics, even when there is no observer, there is a physical reality. But in quantum mechanics, the nature of physical reality depends on the observer who observes that thing.
​
2. Quantum mechanical superposition principle is another unbelievable thing. As far as waves are concerned, it is possible to superpose two waves and make a new wave. Since all material objects also are waves in quantum mechanics, it is possible to superpose them also. We can superpose a living cat and a dead cat and make a new kind of cat!
​
3. Entanglement is a peculiar feature of quantum mechanics. Suppose a particle decays into two particles that go in opposite directions. Standard quantum mechanics says that if the state of one particle is changed, the state of the other particle will change. The two particles may be thousands of kilometres away from each other!
​
Although Einstein was one of the creators of quantum theory, he did not like the above features. He believed that quantum mechanics is not the complete theory and that there is some truth hidden behind it.
​
There were many debates between Bohr and Einstein on quantum mechanics. Bohr could answer many of the questions by Einstein and resolve the contradictions. Nevertheless the debate continues.
​
In 1927, there was an International Conference in Como, Italy. Bohr gave a lecture there. Many eager physicists like Max Born, de Broglie, Heisenberg, Pauli, Dirac and Sommerfeld came to listen to him. In his lecture, Bohr talked about his complementarity principle for the first time. He explained how Heisenberg's uncertainty principle controls the outcomes of experiments. He also discussed how Born's probability interpretation gives the true meaning of Schrodinger's wave function. He combined all these components and established the basis of quantum mechanics. This came to be known as the Copenhagen interpretation.
​
Scientists had believed themselves to be mere observers. But the Copenhagen interpretation of quantum mechanics contradicted this. Observer also became a part of the experiment. Only when the property of a thing is measured, such as its position or momentum, Schrodinger's wave jumps to a particular state. Only when the electron is subjected to experiment, it becomes a real object.
​
Atomic nucleus and World War
After 1935, Bohr directed his attention on the nucleus. There are protons and neutrons inside the nucleus. It is the short-ranged strong force that keeps the protons and neutrons together. Bohr thought of the nucleus as a liquid drop and developed a theory of the nucleus.
​
In 1939, Otto Hahn and Lise Mitner discovered nuclear fission. Bohr could explain many properties of nuclear fission using his liquid drop model.
​
Mitner was a Jew,so there was the the danger of her being expelled from Germany by the Nazis. She escaped to Sweden. Hahn and Meitner pursued their research on fission while working in different countries. Mitner kept Bohr informed of the results of her experiments. Bohr came to know of the enormous amount of energy released in nuclear fission and realized its terrible significance in the context of the war. When Bohr went to USA, he conveyed to Einstein the
information that the German scientists knew enough to make the nuclear bomb.
​
In 1940, Germans occupied Denmark. While remaining in Copenhagen Bohr maintained contact with the British scientists. In 1941, Heisenberg came to meet Bohr. Heisenberg was one of the scientists who remained in Germany and was in a high position. He was involved in the German project to make the bomb. But he told Bohr that he believed Germany and the allies must drop the idea of making the nuclear bomb. Bohr did not believe what Heisenberg said!
​
In September 1943, Bohr came to know that he was about to be arrested. He and his family left in the night and travelled in the darkness to Sweden and then to England. They suffered a lot during this dangerous journey. Reaching England was like a rebirth!
​
From England Bohr went to America and was with the scientists who worked on the Manhattan Project making the bomb. After Bohr had informed Einstein, Einstein warned President Roosevelt about the bomb. Roosevelt permitted the start of the Manhattan project.
​
After the end of the war in 1945, Bohr returned to his Motherland and became the Director of the Copenhagen Institute again. His son Aage Bohr won the Nobel Prize for discoveries related to his father's liquid drop model.
​
In 1960, Niels Bohr came to India. He met Jawaharlal Nehru in Delhi and Homi Bhabha in Bombay. He lectured in the Tata Institute of Fundamental Research.(I listened to that lecture: GR )
​
He was involved in forcefully spreading the message that the knowledge about nuclear weapons must be shared by all the countries of the world.
​
Niels Bohr passed away in 1962, when he was 77.
​
Reference
Ten physicists who transformed our understanding of physical reality, by R Evans and B Clegg, Robinson, Running Press, London, 2015.