01-27-2008, 02:01 AM
[quote Ted King]I did find out information about the wave nature of electrons around a nucleus but I couldn't seem to find information that specifically answered the student's question.
Ted-
First, I want to reiterate how cool it is that you are looking for an answer to your student's question. It shows a level of dedication to teaching that, unfortunately, is not present enough in our nation's schools. It is obvious that you are enthusiastic about what you do and instead of being embarrassed about not knowing the answer, you have used her question as an opportunity to learn something new yourself. Kudos.
I think that Tominator's answer is as good as any you will find using google. The reason that you are not finding a specific easy answer to her question is not because you aren't using the right keywords- it is because there isn't an easy way to explain some things. Understanding what exactly is happening at the quantum level is, quite bluntly, outside the ability of most people. This is truly the realm that only the greatest scientific minds will ever really comprehend.
The rules of Newtonian physics break down at the extreme ends of our everyday world. Go large, small, or fast enough and the things that we intuitively know don't apply. As a physics teacher, I am sure that you know this. So in order to give people a basic understanding of what is happening we use intuitive models that approximate what is really going on. Sometimes these models work well. In this case the first three periods behave pretty well within the Bohr model that Tominator used, but sometimes they don't. As pbarra1 mentioned- even the smartest people don't always agree on what or why things happen the way they do.
As Tominator said in his first post, there are other factors at play including atomic shielding, but even these effects are very difficult to precisely calculate and would require an understanding of the Schrödinger equation or Slater's empirical formulas. In addition, there are complex direct and indirect relativistic effects at play since the electrons are in accelerated motion and therefore the equations of special relatively do not rigorously apply. Also, as atomic mass increases the speed of the innermost electrons approaches the speed of light. Now you are moving into an area the requires a knowledge of relativistic Hamiltonian. You can throw spin-orbit effects into the mix as well. You can see where I am going with this- it is difficult subject matter.
Let me reiterate that in my opinion Tominator's explanation and simplifications are as good as you will probably find on the internet. It is on the level of information that is taught to physics and chemistry students at the bachelor's level. If you want to know more then you will probably need to find a quantum chemist/quantum physicist to explain it. In my experience, the problem that you will undoubtedly encounter is that the people that really understand this stuff usually have a very difficult time explaining it to those of us that don't (see my post above.) Some of the smartest people that I know sat in Dr. Shultz's class for a semester and admitted at the end that they understood about a quarter of what was taught. I understood about 1/10th of the information presented and was glad to take my C+ and move along. And I wasn't a "moron major" either.
I think the central issue here is that a 13 yo was insightful and curious enough to even ask the question. She was obviously thinking at the next level. In my opinion she should be watched closely and nurtured along if she shows an inclination to pursue the sciences. Unfortunately, women are woefully underrepresented in the the hard sciences. While some of this is undoubtedly a genetic predisposition, it has been known for years that boys in America are given preferential treatment in science classes and yet very little has been done to rectify this inequality. There are undoubtedly cultural influences as well since Asian American women do not seem to share the same disparity that is seen among other ethnic groups. This leaves me curious as to what her parents do.
In any case, there are worse ways to spend your Saturday then reading up on quantum mechanics. Admittedly- there are very few people here who would agree with that statement. Here are a couple interesting links:
http://en.wikipedia.org/wiki/Lanthanide_contraction
http://zopyros.ccqc.uga.edu/lec_top/rltvt/node28.html
http://books.google.com/books?id=3stGfWt5XT8C&printsec=frontcover
Craig
Ted-
First, I want to reiterate how cool it is that you are looking for an answer to your student's question. It shows a level of dedication to teaching that, unfortunately, is not present enough in our nation's schools. It is obvious that you are enthusiastic about what you do and instead of being embarrassed about not knowing the answer, you have used her question as an opportunity to learn something new yourself. Kudos.
I think that Tominator's answer is as good as any you will find using google. The reason that you are not finding a specific easy answer to her question is not because you aren't using the right keywords- it is because there isn't an easy way to explain some things. Understanding what exactly is happening at the quantum level is, quite bluntly, outside the ability of most people. This is truly the realm that only the greatest scientific minds will ever really comprehend.
The rules of Newtonian physics break down at the extreme ends of our everyday world. Go large, small, or fast enough and the things that we intuitively know don't apply. As a physics teacher, I am sure that you know this. So in order to give people a basic understanding of what is happening we use intuitive models that approximate what is really going on. Sometimes these models work well. In this case the first three periods behave pretty well within the Bohr model that Tominator used, but sometimes they don't. As pbarra1 mentioned- even the smartest people don't always agree on what or why things happen the way they do.
As Tominator said in his first post, there are other factors at play including atomic shielding, but even these effects are very difficult to precisely calculate and would require an understanding of the Schrödinger equation or Slater's empirical formulas. In addition, there are complex direct and indirect relativistic effects at play since the electrons are in accelerated motion and therefore the equations of special relatively do not rigorously apply. Also, as atomic mass increases the speed of the innermost electrons approaches the speed of light. Now you are moving into an area the requires a knowledge of relativistic Hamiltonian. You can throw spin-orbit effects into the mix as well. You can see where I am going with this- it is difficult subject matter.
Let me reiterate that in my opinion Tominator's explanation and simplifications are as good as you will probably find on the internet. It is on the level of information that is taught to physics and chemistry students at the bachelor's level. If you want to know more then you will probably need to find a quantum chemist/quantum physicist to explain it. In my experience, the problem that you will undoubtedly encounter is that the people that really understand this stuff usually have a very difficult time explaining it to those of us that don't (see my post above.) Some of the smartest people that I know sat in Dr. Shultz's class for a semester and admitted at the end that they understood about a quarter of what was taught. I understood about 1/10th of the information presented and was glad to take my C+ and move along. And I wasn't a "moron major" either.
I think the central issue here is that a 13 yo was insightful and curious enough to even ask the question. She was obviously thinking at the next level. In my opinion she should be watched closely and nurtured along if she shows an inclination to pursue the sciences. Unfortunately, women are woefully underrepresented in the the hard sciences. While some of this is undoubtedly a genetic predisposition, it has been known for years that boys in America are given preferential treatment in science classes and yet very little has been done to rectify this inequality. There are undoubtedly cultural influences as well since Asian American women do not seem to share the same disparity that is seen among other ethnic groups. This leaves me curious as to what her parents do.
In any case, there are worse ways to spend your Saturday then reading up on quantum mechanics. Admittedly- there are very few people here who would agree with that statement. Here are a couple interesting links:
http://en.wikipedia.org/wiki/Lanthanide_contraction
http://zopyros.ccqc.uga.edu/lec_top/rltvt/node28.html
http://books.google.com/books?id=3stGfWt5XT8C&printsec=frontcover
Craig