Important Differences Between Bound and Unbound Electrons

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This is the The Rutherford-Bohr model of an atom. Image by the U.S. EPA

Atoms are constructed of a central nucleus, containing positively-charged protons and uncharged neutrons, and orbiting, negatively-charged electrons, in number equal to the number of protons.

Although an electron carries a charge equivalent (though of opposite polarity) to that of a proton, its mass is a mere 1/1836th that of a proton.

Some mistakenly think the electron isn’t a particle at all, but a cloud. This inaccurate notion doubtless arises from the cloud-like appearance of the probability distribution curve of an electron in its orbit.

At any rate, an electron generally exhibits particle-like properties, and is best mentally envisioned as a particle.

How the particle we call an electron behaves depends upon the condition in which we find it. There are important differences between bound and unbound electrons.

The Free-Moving, Unbound Electron

Pull out a gun and shoot a bullet, and in many ways, an electron is like that bullet.

It has mass — it has momentum. One additional thing the electron has that the bullet does not is charge.

Consistent with classical behavior, an unbound electron can absorb energy in any amount. Such is not the case with an electron bound as part of an atom or atom fragment.

The Restricted, Bound Electron

Atoms can absorb energy in any amount, but the electrons that orbit the atoms or atom fragments, which are no longer separate entities cannot. They only absorb energy in specific or “discrete” amounts. The reality of this was first expressed mathematically, in the case of the simplest hydrogen atom, by physicist Niels Bohr. He developed the mathematical expression that, in essence postulated such discrete behavior. (See image at left.)

Niels Bohr developed this equation. Copyright image by Decoded Science, all rights reserved.

Plug in the values of Z, n, and R, and it becomes apparent E cannot be just any value. Although scientists intended for this equation to explain the hydrogen atom, and it would be self-defeating to apply it to any other atom, the concept of discrete orbiting electron energies applies across the board.

What If Bound Electrons Could Absorb or Emit Energy in Any Amount?

If a bound electron could absorb or emit any amount of energy as it orbited, it would continually lose energy in the process. Eventually, it would spiral into the nucleus. If that were the case, the universe as we know it could not exist.

Consider a lone hydrogen atom placed in an environment where it receives exposure to a variety of energy sources:

Heat energy is applied. The atom picks up additional kinetic energy in the process. The electron goes largely unaffected. Now photons become available. Different photons possess different energies.

It takes a photon of a correct energy, properly located, for the electron to absorb it. If that happens, the electron jumps to a higher energy level, that is an orbital where n>1. If n is higher than 2, it is possible at some point for the unstable, energized electron to lose some or all of its energy, in steps, the n-value decreasing in steps.

Bound and Unbound Electrons: Important Differences

Important differences, then, depend in part upon the creation of a new entity. In binding to an atom, the electron loses some of its identity. It is no longer a separate entity. It no longer acts entirely like an unbound electron. It can absorb and emit only certain specific amounts of energy (sometimes called quanta).

These quantities of energy are associated with photons. Some photons (those in the visible range of the electromagnetic spectrum) are associated with color. Bound electrons play an important role in the colors of nature. Bound electrons also exhibit various behaviors in magnetic fields. Such interactions are important in analytical chemistry and in the field of medicine.

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