Quantum Mechanics of Atoms

PLEASE READ:   So in week 6 we continue to increase of our scrutiny of the physical world by drawing our attention even deeper into the world of atoms and the study of quantum theory. We will discover that the mechanics we learned in Physics part 1 does still apply in many ways BUT also needs some extra help to include a reality so different than what Sir Isaac Newton had to observe in his time. We will find that the act of making measurements and observations actually have us disturbing a system to the extent we become part of the system in the sense we change the conditions of the system. We find that predictions of behavior of a system are not as defined and clear as what we expect when making macroscopic measurements like where a planet is or the flight path of a football. We find ourselves in a world that requires a statistical approach that also limits our ability to know such things as position and momentum perfectly and at the same time. This is known as the Uncertainty Principle.

We also find ourselves in a world where certain conditions must be met and disallow but only for a certain discrete number of possibilities and the probabilities on when and where they can exist. In the Bohr model of hydrogen we find that the electrons are in an orbit around the nucleus. We find that they cannot just be anywhere around the nucleus but only in certain "levels" and with specific properties pertaining to their energy, linear momentum, angular momentum and rotation or spin. We find the simple Bohr model powerful and yet not able to deal effectively with other elements, yet it still gives us an understanding and picture of the atom.

We also find something very odd indeed. That matter actually has wave properties. We saw this last week with light. That light or the photon can be both a particle and a wave. Actually, it is the model we make to understand nature that allows us to call something a particle or a wave. The same is true of matter. We tend to think of matter as this definite object taking a specific amount of space. How then can we use a wave model to describe matter? It goes back to what I said above. If you try to locate a particle so small that you cannot tell but to within only a small uncertainty where it is and how it is, then you might find it easier to make a mathematical formula trying to describe the system. This math is called a wave function. We will look at what a wave function is in the lab this week and see how it helps us predict the behavior of a system when it is on the atomic scale. But what do you ask does that have to do with everyday objects?  We will find out that macroscopic matter could also be described using these wave functions but that they turn out to be very small indeed. That is because looking at a baseball in flight with light from the sun does not alter the momentum of the ball to any degree we can observe, but it does! Light is energy and in the form of either a wave or particle, it is interacting with the ball. Only the effect is so very small we never notice it.

So here we go with the problems for the Week 6 assignment. REMIINDER!!! Some things to remember when setting up your solutions: 1) Be sure to check your units so that they are all compatible. Example, you may find some units in grams or kilograms while you find other entities in meters/sec or km/sec. Choose what units you are required to answer in or if not required what units you choose. The system of MKS is the standard in the course, but that does not mean the problems are given as mixture like cm/s and kg. 2) Double check that your conversions are correct and that you did not make an error by using dimensional analysis in the calculations. Seconds never will equal kilometers for instance. Although I do not weigh this type of error heavily, I want you to use what I call the "Bungler Alarm" which is to sit back and review your answer and see if it makes sense. Example, if a problem was involving a small distance in cm, you would not expect your conversions to bring you hundreds of miles, unless, of course you were asked to find a really big distance. 3) I have already solved all the problems as well as reviewed the answer key provided to me from the university. I check if there are mistakes including if any constants were used incorrectly. This BTW is why I mentioned you should not waste time and search for similar problems on the web. Many times the mistake was not caught and the error in the calculation just propagates. YOU have the ability to do these problems if you read the slides, read the textbook and participate in the discussions. You also have me. That is why I am here, to bring a warm blooded venue to online teaching. AND I WILL BE THERE TO HELP YOU to understand the material and to understand what it is you are being asked to solve.

Question for week 6 -  What does a matter wave truly represent? Also what is the connection between PSI and PSI^2?   After reading my notes above, and viewing the lessons for the week you should start to realize something about the reality of matter and energy. They are one and the same! Think E=mc^2 . Think of matter as very densely packed energy. I will help you start by answering the second question: the wave function PSI allows one, mathematically, to predict to within a limited certainty, the future status of a system. (We do not have a way to directly observe atomic systems). It contains information about the system. PSI has no direct physical meaning, it is a precursor to a more useful function called PSI^2. PSI can be positive and negative in sign. PSI^2 however is the probability of finding a particle in space about the atom, and is only positive in value and "lives" in value between 0 and 1. It is the odds of finding an electron in an atom at a given moment or finding it every at a location in general. This means it gives real physical meaning on position. It will also turn out that because of the Uncertainty Principle, the better you know position the worse you know the momentum, and the better you know momentum the worse you know position. You cannot have both with equal accuracy AT THE SAME TIME! We will explore PSI and PSI^2 in the lab this week.