Probabilities of the Quantum World (Pt-5)

Summarizing the Masterpiece by Daniel Danin

[To refresh, text in such square brackets is my commentary. Rest of it is a faithful documentation of the most fascinating story ever told of the Quantum Revolution]

[At the end of Part-4, Einstein has made the Quanta real; The atom was still doomed to be unstable and we were waiting for Niels Bohr.]

In the autumn of 1911 when Niels Bohr was at the Cavendish laboratory attending Thomson’s lectures the catastrophy of the planetary atom was completely ignored there too. No one at Cambridge took the Rutherford model seriously!

When the historians asked Niels Bohr: “Where you the only one who responded well to it?”, Bohr said,

“Yes, but you see I did not respond to it. I simply believed it.”

[What a profound statement by Bohr. He simply believed the planetary model of the atom. This is the first step towards any long journey of exploration. Belief. Spiritual masters of yester-years and even today’s Masters likeSri Sri Ravi Shankar for example, they all start with giving an experience which then kindles belief. Once the student believes, further exploration (self exploration or guided by the Master) becomes that much easier. Practically, belief unknowingly permeates all through our daily life... We park our car and walk away with a firm belief that it will be there when we return; We put money in the bank with the belief that it will be available to take out when we need it and so on and on.]

In March of 1912 Bohr made a decision to switch from Cambridge to Manchester, from Thomson to Rutherford. The Dane let Bohr go without any qualms, not fully appreciating whom he was losing. Rutherford, in easily accepting Bohr, did not quite appreciate whom he was acquiring. And, of course, he just could not have imagined that the young doctor from Copenhagen would save his doomed atom.

[Who in our lives have we let go without realizing what actually we were letting go? I can only wonder! I will never know. Again and again I have to train myself to look past the superficial and recognize the potential in people that I come face to face with. It is very difficult for me.I have to keep at it. For many years. It is Abhayasa — practice. Practice makes Perfect.]

Bohr appeared in Manchester at the end of March 1912 and by the beginning of May has become an expert on the planetary model of the atom and the alpha and beta rays of radioactive decay. Once a young Hungarian radiochemist George de Hevesey (Bohr’s friend and contemporary) asked the simplest question to Rutherford: “Alpha particles come from the nucleus. This is clear. But where do the beta particles come from?”. Of course Rutherford did not hesitate to answer. Meekly he said,

“Ask Bohr.”

[Did Rutherford believe Bohr at that point? Oh yes!! He would not have said “Ask Bohr” if he had not believed that Bohr actually had a ready answer. It comes back to belief.]

Bohr answered that the beta particles also came from the atomic nucleus! When the nucleus lost a negative electron it increased its positive charge by one and it can be predicted that an atom of the chemical element next to the original element in the Periodic Table should be produced during beta decay. Even that early Bohr understood that the atomic nucleus was a complex laboratory which could produce particles that it did not contain… Almost fifty years later, Niels Bohr said in the Rutherford memorial lecture:

“Early in my stay at Manchester in spring of 1912 I became convinced that the electronic constitution of the Rutherford atom was governed throughout by the quantum of action (the Planck’s constant h).”

Niels Bohr attempted to use the quantum approach [of a minimum atomic size allowed by nature] to explain otherwise classically-inexplicable phenomena. According to the recent prediction by Laurentz, Bhor had become a ‘thinker in a remote corner of the world’. In fact, his actively searching mind was in a ‘remote corner of the world’ even as he moved through the noisy university halls. Niels Bohr amazed his contemporaries by his capacity for inner concentration.

Once he gave a talk to the physicists in Berlin on his quantum ideas. His friend, the well-known experimenter from Gottingen, James Franck, recalled how Bohr found the answers to complicated questions put by his demanding listeners:

“Sometimes he sat there looking practically like an idiot. The face became blank, the limbs hung loosely down, and you wouldn’t recognize him even if you knew him. There was absolutely no sign of life. Then suddenly one could see that a glow went through him, a spark caught light and he said: “Now I understand it…” ”

[Inner concentration. Indeed. That is a gift. A necessary gift to push forward the frontiers of understanding whether Scientific or Spiritual.]

As often happens, Bohr was helped by chance — something that cannot be planned or prepared beforehand. Half a year had passed since Bohr returned from Britain to Denmark. One day in early February 1913 he was talking to his former university friend Hans Hansen about his quantum ‘torment’. He assured Hansen who worked in spectroscopy that he was close to finding the explanation for ‘the properties of matter which depend on the electron system in the atom.’ He named the most important properties: the stability of materials, the chemical reactions, the magnetism…

“But how about the spectra?” asked Hansen hopefully. “How can your theory explain the spectral formulae?”

“The spectral formulae?!” exclaimed Bohr…

Fifty years later Bohr remembered well Hansen’s question and his own bewilderment: “I did not know anything of the spectral formulae”.

Hansen eagerly insisted, “You must look at the formulae. You’ll see the remarkably simple description they give of the spectra.” “I’ll take a look” promised Bohr.

Little did he think that in future he would refer to this moment as a turning point in the history of our knowledge of nature.

[It took three things to come together in harmony… One brilliant mind; One long period of sustained inner concentrated thought and One serendipitous conversation about something unrelated. Thinking flips on a dime and Nature reveals its secret.]

The same day Bohr found in the literature the well known (to all but him!) brief formula derived by Balmer for the hydrogen spectrum. Looking at it he at once recognized that it gave a genuine explanation for the stability of the planetary atom. Bohr later said,

“As soon as I saw Balmer’s formula, the whole thing was immediately clear to me.”

The schoolteacher Johann Balmer certainly did not imagine that when he published his formula in 1885 (the very year Bohr was born), he was providing evidence of fundamental physical laws. The formula was the result of long work and a faith in the regularity of nature: of course there had to be a law governing the multi-colored luminescence of hydrogen gas. The scientist already knew the wavelength (or frequencies of the electromagnetic oscillations) for the spectral lines emitted by this lightest gas. Balmer started a numerical exercise and derived his formula without knowing anything about the radiation mechanisms. He had simply once boasted that he could find a formula establishing a regular relationship between any given four numbers, and in response, a friend gave him the wavelengths of the red, green, blue and violet spectral lines of hydrogen to try and do just that. Balmer pulled off the trick. And for twenty-eight years (up to the beginning of 1913) the brilliant result of his ‘number trick’ remained uninterpreted by physicists.

[This reminds me of words by a famous mathematician from India, Srinivas Ramanujan: The Man Who Knew Infinity. Ramanujan famously once said,

“… an equation has no meaning for me unless it expresses a thought of God.”

Ramanujan’s work on infinite series was used to explain the Event Horizon of Black Holes more than 100 years later. His notebook is displayed alongside Newtown’s Principia Mathematica at the Trinity College library in Cambridge.]

In Balmer’s formula, one quantity — the constant — was deducted from another quantity — the variable and the value of the variable depended on a series of integers. That was all! The integer 3 substituted into the formula yielded the frequency of electromagnetic oscillations for the red spectral line. The integer 4 yielded the frequency of green light, 5 yielded the blue line frequency, 6 the violet line frequency. Other integers yielded frequencies of lines in the ultraviolet spectrum invisible to the human eye.

Having seen the Balmer formula, Bohr could not tear his eyes from it — he finally understood. Bohr realized immediately that the atom’s energy did not vary continuously but in steps so that it had levels like a house has storeys. Bohr’s discovery was that the atom had stepwise sequence of energy levels.

[Here again, the classical continuous was being quantized or discretized.]

Bohr proposed that the atom has the lowest stable state with non zero energy. Since it is the revolving electrons that emit radiation in the atom, this means that they do not lose the energy of their motion completely — as yet unknown laws prevent them from falling into the nucleus. If this were not the case, the constant in the Balmer formula — the atom energy after emission — would not be finite, it would be replaced with zero, with nothing.

Bohr told historians that two to three days after receiving this advice from Hansen, he again met the spectroscopist to explain to him ‘how the spectra were born’. Now it was Bohr’s turn to say: “Look, isn’t it like this?” — and Hansen’s turn to be confused. But what did confuse the spectroscopist Hansen?

Each step of this ladder is a certain energy level of the atom. [We now know these to be orbitals.] The farther the step is from the nucleus the higher is the level of energy. Like a stone carried up to the tenth storey of a house has higher energy than a similar stone taken to the third storey. The atom is stable at each such energy level, until, it emits a quantum of light. When it emits this energy portion, it drops to a lower stable level in a single jump, without any stop-overs…

That is why Hansen was confused — the picture was too anti-classical. It was long known in classical physics that the frequency of radiation emitted by a body is equal to the frequency of the motion of changes in it. That is a well-known fact. It was not questioned either by Maxwell or Hertz in the last century, or by Lorentz, or Planck in this century. It is no wonder that young Hansen who had not even gained his doctor’s degree was bewildered (and he as preparing for a degree in spectroscopy, so the new theory meant he had to learn much over again).

Only Einstein questioned the traditional concept. However, he never voiced any doubts until the Bohr theory appeared. When in September 1913 Hevesy had a chance to tell him about the experimental verification of the Bohr concept, Einstein exclaimed:

“Then the frequency of the light does not depend at all on the frequency of the electron? … And this is an enormous achievement. In that case the theory of Bohr must be right.”

When the Physicist Einstein wanted to explain that there was no direct cause of relationship between the frequency of rotation of the electron and the frequency of emitted light, the Philosopher Einstein stopped his ‘twin’ and did not allow him to dare. This was founded on absolute belief that nature was governed by laws of definite determinancy. After some years he formulated his classical belief in the well-known joke:

“I do not believe that God plays dice!”

Nevertheless, Einstein the physicist rejoiced to see ideas close to his own embodied in the theory of the atom: “This is an enormous achievement…!”

Niels Bohr, who only recently had known nothing of the Balmer formula was understandably keen to analyze all such formulae accumulated in optics. Following the Swiss school teacher, the scientists used this formula to describe the sequence of frequencies in other series of spectral lines, not only those of the hydrogen atom. The most recent and most general formula derived by Walther Ritx gave such a description for spectral lines.

One can imagine the increasing delight of the quiet Dane as he repeatedly obtained confirmation of his theory: the spectral lines were always found as a combination of two quantities with a minus sign between them!

The Ritz formula had a new feature that the Balmer formula lacked. Both quantities — the atom energies after and before the emission — proved to be variable and both dependent on the series of integers. But Bohr expected that. It meant that the electrons emitting the quanta did not have to drop each and every time to the lowest step of the energy ladder. The electron from an upper level could drop to any intermediate orbit allowed by nature and rotate stably along it.

“This is the atom that Bohr built.”

The first electron orbit in the Bohr atom lies high above the nucleus and the space between the nucleus and this orbit is ‘out of bounds’ for the electron — it is not allowed to go there. Bohr managed to calculate the size of this ground state; it was the order of 10^-8 cm.

Another number that made a great impression was 190,000: that was the value obtained by Bohr for the spectroscopic constant appearing in all spectral formulae, and known as the Rydberg constant. Its experimentally measured value turned out to be 109,675.

Rutherford posed the most penetrating question which for the first time raised the significant suspicion: does the quantum theory provide the tiny particle, the electron, with ‘freedom of will’?…

“There appears to me one grave difficulty in your hypothesis, which I have no doubt you fully realize, namely, how does an electron decide what frequency it is going to vibrate at when it passes from one stationary state to the other? It seems to me that you would have to assume that the electron knows beforehand where it is going to stop.”

The answer to this question stumped Bohr. We will need to wait for Louis de Broglie to appear on the scene next…

… To be Continued

[Oh ya… for the Medium uninitiated, please leave a couple of “claps” below if you like this and would be interested in the subsequent part(s). Thanks.]

By training a PhD Chemical Engineer from IIT Bombay; By passion a volunteer Meditation Instructor with the Art of Living Foundation.