Chapter 31: Atomic Physics
Applications

Creating New Views of Nature

Niels Bohr And The Beginning of The Quantum Theory

What is a theory?

A physical theory is a particular view of nature. A physical theory attempts to explain a set of human experiences and observations in terms of a few basic facts and rules. A good theory presents a wide range of experiences as logical consequences of a few fundamental rules applied to a few fundamental facts. Newton's theory of gravitation explains diverse and seemingly unrelated phenomena such as tides and eclipses as consequences of the fact that all material objects in the universe attract one another (the gravitational force) and that these objects obey the rules of mechanics (Newton's Laws of Motion.)
New theories are created from a mix of experimental observations , previous theories and new insight. To be accepted by the scientific community, a new theory has to explain the known facts and correctly predict some new observations, the more surprising the better.

Isaac Newton knew that objects released at the surface of the Earth accelerate downward. He also knew that the Moon circles the Earth. He knew the magnitude of the free fall acceleration at the surface of the Earth and he knew the distance from the Earth to the Moon. He conjectured that the same kind of force that accelerates an apple downwards also pulls the Moon towards the Earth.
The reason the Moon fails to fall to the Earth is because it is moving just fast enough to maintain the same distance. Consider the Moon at point A in orbit around the Earth. In the absence of the Earth's gravity the Moon would continue along the straight line towards point B. Because of the Earth's gravity it moves to point C. From the orbital data Newton calculated the gravitational acceleration at the Moon's orbit and compared that to g at the surface of the Earth (9.8 m/s².) He found that the surface value was proportionally larger as the squares of the distances. Newton then stated his theory of universal gravitation from which followed the motions of the known planets (known facts) and which predicted the existence of a previously unknown planet Neptune.

The beginning of the quantum theory

One of the most famous physicists of this century was Richard Feynman, best known to most people for his role in the Challenger disaster investigation. He once wrote:
" If, in some cataclysm, all scientific knowledge were to be destroyed, and only one sentence passed on to the next generation of creatures, what statement would contain the most information in the fewest words? .... All things are made of atoms-little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed one into another."
Nature is grainy. Matter and interactions are quantized.
Quantum theory is THE physical theory of this century. Together with Einstein's theory of relativity it has guided the progress of science and technology.
One of the starting points of the quantum theory is Niels Bohr's description of the hydrogen atom. As we review how Bohr constructed his theory of the hydrogen atom we can see the interplay of the three ingredients that create a new theory:

known observed facts,
previous theories
and new insight.

1. Known facts.

When Niels Bohr joined the laboratory of Ernest Rutherford in 1912 he knew that the spectra of atomic gases, such as Hydrogen and Helium, contain a highly restricted set of colors, whereas the spectrum of radiating solid, such as a light bulb filament, contain virtually all the colors. This is illustrated in the image to the left. It shows the view of a light bulb filament through an inexpensive optical grating. Just below the filament is a view of a thin gas discharge tube through the same grating. The spectra of gases are discrete.

Bohr also knew of the existence of charged particles called electrons (which are emitted by hot metals for example). He knew the mass and the charge of an electron. He also knew that some metals will emit electrons when illuminated by short wavelength light (even weak light) but will not emit electrons when illuminated by long wavelength light (even when very intense.) This was known as the photoelectric effect.

2. Previous Theories.

Bohr was a trained physicist, familiar with classical mechanics and electricity and magnetism, much as you are if you have read this far in Giancoli. He also knew of the recent (1905) theory of the photoelectric effect proposed by Albert Einstein: a beam of light is made up of small packets of energy called photons.

Blue light photons are more energetic than red light photons. When an electron is ejected from an illuminated metal surface it gets its energy from a single photon. Thus even very intense (lots of photons) light of the wrong wavelength (individual photons too wimpy) cannot eject electrons. Similarly, weak ultraviolet light will cause a sunburn, but intense sunlight passing through glass (which blocks UV) will not.
Bohr was also familiar with Rutherford's idea of the nuclear atom. Atoms are not solid. They are made up a positively charge nuclei and electrons which orbit the nucleus, much as the planets orbit the sun. The electrons are in motion, so they posses kinetic energy. The electrons are also under the influence of the attractive force of the nucleus, so they posses potential energy. The sum of these two energies determines the orbit of a particular electron.

To review again the items from which Bohr created his theory.

An atom consists of a positive nucleus and one or more electron in orbits around it. In each orbit the electron has a definite amount of energy.
Atoms can be made to emit light. The set of frequencies of light, emitted by atoms of a gas such as hydrogen is restricted to a well known set.
Light is a stream of energy packets, called photons.
Individual photons possess an amount of energy which is proportional to the frequency according to the Einstein formula E = hf.

3. New insight.

Now for Bohr's insight:

An atom emits one photon at a time
The energy gained by the photon is energy lost by the orbiting electron as it shifts from one orbit to another, closer to the nucleus.
Nature restricts the possible orbits of an electron to a well defined set. (Note: This is new. It does not follow from any of the theories of Bohr's time)
Bohr specifies that the ANGULAR MOMENTUM of the electron as it orbits around the nucleus has to be multiple of the fundamental constant h. (also new, does not follow from any of the theories of Bohr's time.)

Using these ideas Bohr calculated the frequencies of the photons emitted from hydrogen. His calculated values agrees with the observed values, which were known to a very high precision. Bohr received the Nobel Prize in 1922.

How about the requirement that the new theory predict a new observation. Bohr's theory did not meet that requirement. In fact, Bohr's theory fails when applied to atoms other than hydrogen.

Was it a useless exercise? Bohr's notion that the energies of the electron in an atom must be restricted (quantized) in some way was picked up by other physicists who based the quantum theory on very insightful mathematics. This theory forms the basis of twentieth century chemistry and is being extended to explain the microscopic properties of materials. Bohr contributed mightily to the interpretation of the quantum theory in ways that are still controversial.
The mathematics of the quantum theory yields result which agree remarkably with observed facts, but the mathematical constructs also seem to imply that some phenomena in the small world of subatomic particles are not completely determined before they happen. This did not please Albert Einstein who discussed the issue with Niels Bohr on several occasions in the now famous Bohr-Einstein debates. The famous statement of Einstein's: "God Does Not Play Dice With The Universe" comes from these debates.

Even though Bohr's theory of the atom is now a scientific relic, it has served as one of the springboards for the development of twentieth century physics. It is a beautiful example of the theory building process.

Some Further Study Links:

1.The Scientific Method.

2. The Quantum Theory.

3. More on the nuclear atom.

4. More on The Quantum Theory.