THE PROBABILISTIC INTERPRETATION OF ATOMIC ORBITALS


MATERIALS REQUIRED

INTRODUCTION

The purpose of this exercise is to increase your familiarity with the wave functions of the hydrogen atom and how they relate to the probability function and electronic distribution. In an earlier "dry lab", you studied electrons as being physical objects having mass, charge, and occupying a specific position in space (The Bohr Model.) The last part of this dry lab introduced the concept of a wave associated with a moving particle. Modern quantum theory does not treat electrons as particles at all, but rather as waves. This is analogous to the different theories on the nature of light that you may already have encountered in physics. Wave behaviour has been well studied and is easy to express mathematically by "wave functions". With light, you will recall, a simple sine wave function is used. Electronic wave functions are somewhat more complex but may still be defined mathematically. They are given the symbol y (psi). In the computer simulations of this experiment, hydrogen-like orbitals are used, because these are the only functions which can be exactly calculated.

PROCEDURE

The first "applet" is based on the following hypothetical experiment, and represents one of two interpretations of the quantity (y2). This interpretation treats the electron as a localized particle, moving somewhat randomly, but more likely to be found in certain regions of space than others according to the wave function describing it.

Imagine that someone has invented a super-powerful microscope attached to a camera. With this microscope we can actually see electrons, but the "depth-of-field" of the microscope is so shallow that it can only focus in one plane, the xy plane i.e. with z = 0, and only electrons appearing on, or very near this plane, are going to be seen. Every few milliseconds or so, a new exposure is made, but always on the same piece of film. If electron happens to be in the xy plane, its position is recorded as a dot on the film. As time passes, regions where most "sightings" are made will be thickly sprinkled with dots, while regions where the electron is not so likely to be seen remain dark. Eventually the brightness of a particular region indicates the probability that the electron will be found there. The diagram to the left of the applet which you will find below shows the results of this "experiment".

The histogram, a particular type of graph showing distributions, which is shown to the right of the diagram of the electron sightings, plots the number of these sightings as a function of distance from the nucleus in small increments.

Using the applet

Select orbitals by clicking on their buttons. (Please note that the labels on the buttons are not correctly written, for example 2px is written 2px because the subscripts cannot easily reproduced. In your report, you should write them correctly.) Also note that some of the orbitals cannot be displayed in this applet: think about why!

You can start to work on a new orbital whenever you like by making another choice. Initially, by default, a sighting will be recorded each time you click on the "Shutter" button. Clicking in the "Auto" box makes the program run automatically, marking sightings as quickly as the program can generate them. You can stop this any time you like by clicking on the "Shutter" button. Allow the diagrams to develop for several minutes until you are sure of their appearance.



Exercise 1: On distinguishing random "noise" from real effects

Sketch the electron scatter diagram and the histogram for each orbital and hand them in with your report. Also, describe them in words distinguishing between those features which are significant and will be common to repeated runs on the same orbital, and those which are not.

Exercise 2: On probability and the Heisenberg principle

Contrast these results with the Bohr model that you studied in Experiment D1: what features of Bohr orbits are uncertain, and which are exactly defined. Which features of the orbitals you have been observing are uncertain and which, if you watch long enough, would be exactly reproduced on each run.


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