Re: How long does it take for an electron to jump orbits.

Hello Vincent.

Your question is short and concise, which is good: “How long does it take 
for an electron to jump orbits?”

Since there are lots of different states for an electron, however, there 
can be many answers to the question.  Plus, there are several mechanisms 
that can drive an electron to jump from one state to another.  That 
complicates things further.  Plus, we’re talking about quantum mechanics, 
which is so complicated nobody can claim to understand it!

To tackle your question, let me say right now I’m going to limit the 
discussion to transitions involving light, or photons, and I’ll give 
direct answers for two very different cases.  At the end I give you an 
absolute minimum transition time, followed by a physical description of 
why that is.

The first case is that of an excited hydrogen atom, decaying spontaneously 
to the ground state.  For an electron in the 2p state, it decays to the 1s 
state (the ground state) in 1.6 x 10^-9 seconds, or 1.6 nanoseconds.

By ‘electron in the 2p state,’ I’m referring to a specific excited state 
of the hydrogen electron, which happens to be the third-highest state of 
the electron.  In the decay process a photon of energy 10.2 electron volts 
is emitted, which is an ultraviolet photon of wavelength 121.5 
nanometers.  The photon has this energy because of energy conservation: 
10.2 eV is the energy difference between the 2p and 1s electron states.

NOTE: 1.6 ns is the AVERAGE decay time.  Transitions involving photons are 
probabilistic processes, so two identically-prepared atoms will generally 
decay at two different times.  If you measured a whole bunch of atoms, 
resolving the photons emitted as a function of time, you would find the 
emission intensity to start strongest right away and decay exponentially 
with the 1.6 ns time constant.

This was a specific example, involving a transition accompanied by a 
single photon of light.  Most electrons which decay this way will decay in 
roughly the same time frame.  So, one answer to your question is that it 
takes a few nanoseconds for an electron to jump orbits.

However, transitions can take much longer.  An electron in the second-
highest state of the hydrogen atom, the 2s state, has an average decay 
time of 1/7 of a second.  In other words, the 2s state lasts over 140 
million times longer than the 2p state, even though the two states are 
similar.  The reason it takes so long is that the decay process is 
different – quantum mechanics says that the electron cannot go from 2s to 
1s via a single photon.  The process involves two photons and a much lower 
probability.  Hence, the longer lifetime.

I can give you an absolute lower bound on the time it takes to make a 
transition.  For an electron to transfer from one state to another via 
light, it will have to take at least as long as several oscillations of 
the light wave.  [The oscillation period T of a light wave is the inverse 
of its frequency F.  F is related to the speed of light c and the 
wavelength of light L via the relationship:  c = L F.  So:  T = L / c]

It’s easy to picture why in the case of spontaneous emission.  When the 
light is emitted, you can imagine it is being generated from the electron 
wiggling back and forth at the same frequency as the emitted light.  Since 
emitted light must have some frequency, the wiggling has to last at least 
as long as it takes to trace out several optical oscillations.

In our example of the 2p-1s transition, the oscillation period T was (121 
nm / c) = 4 x 10^-16 seconds = 0.4 femtoseconds.  Obviously, this is much 
less than the transition time.  On average, the electron ‘wiggles’ back 
and forth (1.6 ns / 0.4 fs) = (4 million) times before it settles down.  
As with most cases you find, this is nowhere near the minimum transition 
time.

If you’re interested in more details, you may want to explore the 
following site which lays out the math behind electron transitions, 
accompanied by some neat animations:
 http://jchemed.chem.wisc.edu/JCEWWW/Articles/DynaPub/DynaPub.html

The home page for that document (and others) is found at:
 http://jchemed.chem.wisc.edu/JCEWWW/Articles/index.html


You can also find similar answered questions at:
 http://www.madsci.org/posts/archives/oct2000/972676418.Ph.r.html
 http://www.newton.dep.anl.gov/askasci/phy00/phy00608.htm