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

Date: Fri Apr 16 09:21:35 2004
Posted By: Guy Beadie, Staff, Optical sciences, Naval Research Lab
Area of science: Physics
ID: 1081007427.Ph
Message:
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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

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

http://jchemed.chem.wisc.edu/JCEWWW/Articles/index.html

You can also find similar answered questions at:

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