Day 3 – Bohr’s Atom, Schrodinger’s Cat, Heisenberg’s Uncertainty & Witten’s Branes

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· In the Bohr Model the neutrons and protons (symbolized by red and blue balls in the adjacent image) occupy a dense central region called the nucleus, and the electrons orbit the nucleus much like planets orbiting the Sun (but the orbits are not confined to a plane as is approximately true in the Solar System).

· The adjacent image is not to scale since in the realistic case the radius of the nucleus is about 100,000 times smaller than the radius of the entire atom,

· electrons are point particles without a physical extent.

· This similarity between a planetary model and the Bohr Model of the atom ultimately arises because the attractive gravitational force in a solar system and the attractive Coulomb (electrical) force between the positively charged nucleus and the negatively charged electrons in an atom are mathematically of the same form.

· (The form is the same, but the intrinsic strength of the Coulomb interaction is much larger than that of the gravitational interaction; in addition, there are positive and negative electrical charges so the Coulomb interaction can be either attractive or repulsive, but gravitation is always attractive in our present Universe.)

But the Orbits Are Quantized

Quantized energy levels in hydrogen

1. The basic feature of quantum mechanics that is incorporated in the Bohr Model and that is completely different from the analogous planetary model is that the energy of the particles in the Bohr atom is restricted to certain discrete values. One says that the energy is quantized. This means that only certain orbits with certain radii are allowed; orbits in between simply don't exist.

2.

3. These levels are labeled by an integer n that is called a quantum number. The lowest energy state is generally termed the ground state. The states with successively more energy than the ground state are called the first excited state, the second excited state, and so on. Beyond an energy called the ionization potential the single electron of the hydrogen atom is no longer bound to the atom. Then the energy levels form a continuum. In the case of hydrogen, this continuum starts at 13.6 eV above the ground state ("eV" stands for "electron-Volt", a common unit of energy in atomic physics).

Although this behavior may seem strange to our minds that are trained from birth by watching phenomena in the macroscopic world, this is the way things behave in the strange world of the quantum that holds sway at the atomic level.

Atomic Excitation and De-excitation

Atoms can make transitions between the orbits allowed by quantum mechanics by absorbing or emitting exactly the energy difference between the orbits. The following figure shows an atomic excitation cause by absorption of a photon and an atomic de-excitation caused by emission of a photon.

In each case the wavelength of the emitted or absorbed light is exactly such that the photon carries the energy difference between the two orbits. This energy may be calculated by dividing the product of the Planck constant and the speed of light hc by the wavelength of the light). Thus, an atom can absorb or emit only certain discrete wavelengths (or equivalently, frequencies or energies).

However there were concepts in the new quantum theory which gave major worries to many leading physicists. Einstein, in particular, worried about the element of 'chance' which had entered physics. In fact Rutherford had introduced spontaneous effect when discussing radio-active decay in 1900. In 1924 Einstein wrote:-

There are therefore now two theories of light, both indispensable, and - as one must admit today despite twenty years of tremendous effort on the part of theoretical physicists - without any logical connection.

The Elegant Universe is a NOVA special that is excellent at describing the current quandary of physics and string theory.

http://www.pbs.org/wgbh/nova/elegant/program.html

It is available free from this link. (Thank you, Joshua for the reference!)

Day 3 –Homework – Bohr’s Atom, Schrodinger’s Cat, Heisenberg’s Uncertainty & Witten’s Branes

1. Using the atomic models described by John Dalton, J.J. Thomson, Ernest Rutherford, Neils Bohr and Louis de Broglie and Erwin Schrodinger, what elements are the same? What elements differ?

2. What does it mean to have Quantized Energy Levels? How does this effect where an electron will be?

3. What force is described in the QED theory?

4. What force is described in the QCD theory?

5. Describe Schrodinger’s Cat Paradox. Why is this model used everywhere in the Quantum world?

6. Look up the Dirac Equation of 1928 and describe why it was so important to Quantum Mechanics.

7. Why is string theory so novel? What are some of the assumptions that the theory makes that will cause testing the theory to be difficult? What are some of the dangers of string theory?

8. What is the difference between fermions and a bosons?

9. What is Heisenberg’s Uncertainty Principle?