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Energy at the sub-molecular level (2013)

Page history last edited by Joe Redish 2 years, 9 months ago

Working ContentEnergy: The Quantity of Motion

 

Prerequisites

 

We have developed the concepts of mechanical energy by looking at the motion of physical objects at the human level. This has led us to the ideas of something that is associated with motion that we call kinetic energy -- the energy of movement (½mv2), and potential energy -- the energy of interaction (and relative place or position). It turns out that as we turn to a consideration of the molecular and atomic level, these concepts still apply, though with some additional factors.

 

Resistive forces and thermal energy

One of the things that we learned was that our macroscopic mechanical energy -- kinetic plus potential -- was only conserved if resistive forces (friction, viscosity, drag) could be ignored. If they could not be ignored, the total mechanical energy was drained -- lost as the motion went on. And from considerations of examples with a rapid loss of mechanical energy, we concluded that the lost energy actually went somewhere -- into raising the temperature of the interacting matter. We will see that increased temperatures correspond to the increased (chaotic) motion of the molecules of the matter. With this perspective, the apparent loss of mechanical energy due to resistive forces can be seen as still conserving mechanical energy, just transforming it from a coherent motion (all the molecules of the object moving in the same direction) to a random and incoherent one (all the molecules of the object moving every which way).

 

But the atomic/molecular perspective doesn't only restore our conservation of mechanical energy. It also transforms the way we think about energy.

 

Kinetic and potential energy in an atom or molecule

As you know from your chemistry class, atoms are made up of small dense nuclei (protons and neutrons) that contain most of the atom's mass, and light, fast moving electrons that determine the atom's size. Electrons, protons, and neutrons don't behave like tiny billiard balls. Rather, they have complex properties that are both particle-like and wave-like.

 

Once nuclei and electrons combine to build up an atom, the motion of the atom is, in most circumstances, well described by the classical Newtonian framework we have been studying. But within the atom, and in the binding interactions of atoms into molecules by the sharing of electrons, the rules of quantum physics need to be used.

 

In quantum physics, electrons and nuclei still have kinetic and potential energies that add up to a total energy, but at any given instant of time one can't say that an electron has a particular position or velocity -- and as a result one can't say that it has a particular potential or kinetic energy. Electrons (and other objects for which quantum effects are significant) have to be thought of as being capable of being in multiple places and states at the same time. So we will describe the potential energy of an electron and what its associated kinetic energy is. We can even think of it in the same way as any classical particle moving in a potential well.  But there are a couple of funny factors that have to be added: quantized energy levels and barrier penetration.

 

Quantized energy levels

Because electrons behave at some level like waves, the waves have to "fit" into possible orbits. One result is that not all states are allowed for electrons in an atom or molecule. There are certain discrete "energy levels" that are permitted by the laws of quantum physics. The same thing is true of atoms bound into molecules -- though there the effect is less important, since the spacing of the levels depends inversely on the size.  It's most important for electrons, less important for molecules. But it provides some valuable tools since the absorption and emission of light is restricted to going between allowed levels and that gives a distinct pattern of absorption and emission that are characteristic of individual atoms and molecules.

 

Barrier penetration

One of the properties of describing motion in terms of energies is that it was easy to determine the endpoints. When the KE goes to 0 the object stops. Furthermore, the object will never be found in a region in which the KE is negative. In atomic and sub-atomic physics this is not strictly true. An electron can be found in a region where its KE would be negative and it can penetrate through a barrier that would be an absolute wall classically. The probability that this happens goes down -- very fast -- as the barrier gets larger, so don't expect to walk though a wall any time soon!

 

Chemical processes that are important for biology are often prevented from happening by a potential energy barrier. The presence of various catalysts can be used to change the height of the barrier to turn a reaction off or on.

 

Transferring energy: Collisions and photons

We've mostly looked at situations in which mechanical energy is either conserved or lost to hidden internal degrees of freedom -- the thermal motion of atoms and molecules. But when we consider the motion of atoms and molecules themselves, we have to consider explicitly the way they can exchange -- gain or lose -- energy with other objects in their environment. There are two primary mechanisms by which they do this: collisions with other objects and the absorption or emission of electromagnetic energy -- photons.

 

Atomic and molecular collisions

When two atoms or molecules are interacting, they can exchange energy by colliding with other atoms or molecules. A nice example of how this works is given in the simulation of molecular interactions from the CLUE project (requires Flash).

 

Photons

Electromagnetic energy -- light, radio waves, X-rays -- also has quantum properties. It can be described as made up of little packets of energy with the energy proportional to the frequency. Molecular states can be changed by the absorption of electromagnetic energy. For example, the absorption of photons by molecules of chlorophyll is the way the energy of the sun is transformed to fuel all life on earth. The absorption of light by molecules of rhodopsin is the basic chemical mechanism by which our bodies create signals that we can interpret as vision.

 

Follow-ons:

 

Workout:

                

 

Joe Redish 11/15/11

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