Re: How long does it take for electron to change energy levels?

Hi Andrew,

With quantum mechanics, it's not always valid to ask exactly where something is and how fast it is moving, or how much energy it has at what time---this is due to Heisenberg's Uncertainty Principle. Some people will explain Heisenberg to you by showing a photon hitting an electron and making it move, then saying "the measurement affects the thing you're trying to measure." This is a misleading description; a better explanation is that every object is in multiple locations/energies/momenta at the same time, and only settles into one of them after interacting with something else.

When an electron jumps up one energy level, it starts off in the lower energy level (let's say this has energy E = 1 eV), then a short time later it can be found in the higher level (say with energy 2 eV). What happens in between? Well, there's some period of time where the electron is in both the 1 eV and 2 eV levels; then eventually the electron is just in the 2 eV level. This is called a "superposition" or a "mixed state".

In principle, a mixed state can last for a fairly long time---this is an important aspect of the "quantum computers" which physicists are trying to develop---although I'm not sure how long such states can be practically maintained in excited atoms. However, you can use Heisenberg's Uncertainty Principle to estimate the shortest possible time that the electron can be in the mixed state. One version of Heisenberg's Principle is dP dX > hbar/2: the uncertainty in position (dX) times the uncertainty in momentum (dP) must be larger than hbar/2, or 3.3 x 10^-16 eV*s. It is equivalent, however, to say dE dt > hbar/2: the uncertainty in energy dE times the uncertainty in time dt is greater than hbar/2. In the example above, where the energy is (briefly) uncertain within a range of 1 eV, the state will generally have a lifetime longer than 3.3 x 10^-16 seconds.

Perhaps a more intuitive way to think about it is to learn about wave mechanics. The electron's "real state" is something called a wavefunction; this wavefunction describes probable locations, energies, etc., rather than actual ones, but it still evolves according to Schrodinger's Equation. Schrodinger's Equation is a wave equation, and the wavefunction's behavior is intuitively rather similar to the behavior of water waves, light waves, waves on rippling fabric, etc., that obey similar-looking equations. The "1 eV state" means that the electron's wavefunction has a certain pattern to it; the "2 eV state" is another pattern. When the atom is hit by (or releases) a photon, you can think about this distorting the original wave pattern; the distortions propagate at the ordinary wave speed and in ordinary wavelike ways. The electron can be said to be "in the 2 eV state" when the transient, distorted wave pattern happens to look more like the 2 eV pattern than like the 1 eV pattern; something called "wavefunction collapse" makes it settle into exactly the 2 eV state rather than remaining in the weird state; this "collapse" is what makes quantum mechanics weird and counterintuitive. Does that give you a clearer mental picture?

Hope this helps,

-Ben