Quantum Fuzz by Michael S. Walker

Quantum Fuzz by Michael S. Walker

Author:Michael S. Walker
Language: eng
Format: epub
ISBN: 9781633882409
Publisher: Prometheus Books
Published: 2017-01-11T05:00:00+00:00


We are now going to demonstrate this using a thought experiment. Imagine that we hook the two batteries together in series (negative terminal of one to the positive terminal of the other) so that with the two of them we have a total of eighteen volts. Scientists call that an “electric potential” of eighteen volts. Now if we could attract a single electron to move from the unconnected negative terminal of one of the batteries to the positive terminal of the other battery (at its electric potential of eighteen volts), we could impart an energy to the electron of eighteen electron volts; in scientific shorthand, that is 18 eV. If we moved two electrons, we would provide an energy of 36 eV. It's that simple. (The e in “eV” refers to the charge on the electron. When a charge is moved by an electric potential, whether it's the charge on an electron or something else, it acquires energy that can be measured in electron volts.)

The solution to Schrödinger's equation gives –13.60 eV as the n = 1 energy level of the electron in hydrogen's fundamental most tightly bound, 1s state, its ground state (probability cloud shown at the bottom left of Fig. 3.8). With our batteries, we could provide an 18eV energy boost that would not only lift the electron free of the hydrogen atom but also leave it with an extra 4.4 eV of kinetic energy so that it could speed off to somewhere else.

Now let's examine the energy levels in the rest of the spatial states of the electron in the hydrogen atom. These include the bound spatial states, some of which are represented by the probability-cloud cross sections displayed in Figure 3.8.

As part of the solutions to his equation, Schrödinger found that each bound state for the electron in hydrogen has a total negative energy at only one of an infinite number of possible discrete allowed energy levels characterized by the so-called primary quantum numbers labeled generally by the symbol n. His solutions provide that n can only equal the integers 1, 2, 3, or 4, and so on. These are the numbers shown before the letters above the probability-cloud cross section representations for some of the individual states in Figure 3.8. (They are also the energy quantum numbers for the atomic orbits of the Bohr model constructed in the early days of the development of the theory.) Note that there can be more than one state at each energy level, as will be discussed a bit further on in this chapter.

The solved-for energy of each energy level is –13.60 eV divided by n2, so at each successive energy level the energy gets to be less negative. (That is because negative 13.60 eV is being divided by an increasingly larger squared integer.) So, calculating the energies for the first seven levels, we find the following, starting with the highest level (having the smallest negative energy) with states that least tightly bind the electron. For energy level:

n = 7 the energy of every state is (–13.



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