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Name: Joe B.
Status: student
Age: 17
Location: N/A
Country: N/A
Date: 2001 - 2002

First a couple givens:

1. To find the energy on an electron in a specific atom in a certain energy shell we use the equation E=(-k(Z^2))/(n^2)

2. We can use this to find the energy released when we move an electron from the 1st shell to the 4th shell.

3. E is given in negative energy, as in the amount of energy that is lost because the electron is in that shell captured by the atom. (and because each shell can only hold so much energy so some must be lost for an electron to enter that shell)

4. Einstin's (E=mc^2) says that as the speed increases so does the mass. This means that the amount of energy increases without bound to infinity.

Now my question:
My Chemistry teacher says that a free atom (not one attached with an atom) has an infinite amount of energy. How can this be? If the electron has an infinite amount of energy and it take an infinite amount of energy to go at or above the speed of light wouldn't the electron be able to go faster than the speed of light or be able to power something else to go faster than the speed of light? Doesn't this break Einstine's theory of relativity? I don't agree that a free atom has infinite energy. Where did that come from???

It is conventional to choose as the "zero" of energy of an atomic state the energy of the atom and an electron separated by a long distance (we say infinite, but everyone agrees that the convention means large with respect to the electron / nuclear distance. The only "absolute energy" that you can assign to an atom (or any other particle(s) is its mass multiplied by c^2. But because this number is so large compared to all the other energy differences of interest in atomic and molecular computations and measurements, other "zero" energies are mutually agreed upon, otherwise we would always be taking the differences of to very large numbers, which is inconvenient.

Vince Calder

Simple: a free electron does not have an infinite amount of energy. In fact, a free electron at rest is considered to have zero energy. If it is captured by a nucleus, its energy becomes negative, so some energy has to be released to the surroundings.

Richard E. Barrans Jr., Ph.D.
Assistant Director
PG Research Foundation, Darien, Illinois


This may be a case of misunderstanding ....

I think what your chemistry teacher means is that a free atom (not one attached with an atom) has an infinite 'energy level', meaning that 'n', not 'E', in the equation below is infinite. This results in an energy of 0. I.E., the state in which the electron is not bound to a nucleus is the reference point for the energy measurements. For the electron to bind to a nucleus and it must lose energy. Alternatively, if you add energy to it, it is velocity must increase.

Greg Bradburn

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