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Name: Ayed R.
Status: student
Age: 20s
Location: N/A
Country: N/A
Date: 1/13/2003

What is the time that the electron need to jump from one energy state to the next energy state?

Yours is a very subtle question (or let us say the answer is). Quantum mechanics tells us a lot about the properties of various energy levels, but not very much about what happens in between. The lifetime of some excited states can be measured. They vary from nano seconds to hours. Here is how its done (simplified)"

Suppose a molecule or atom has three (or more) electronic states: E0, E1, E2, ... with different energies:

E0 < E1 < E2 < ...

If the sample is exposed to radiation of energy (or frequency, because E = h*nu, where 'h' = Planck's constant and 'nu' is the frequency) having an energy equal to E2 - E0 the excited state may decay by a transition(s) E2 ----> E1 ----> E0 or E2 ----> E0. One then uses a spectrometer to monitor the intensity vs. time of the cascade of energy levels (frequencies). This gives you the lifetimes of the various electronic states.

Now if you mean the transition lifetime, that is, the time it takes for an electron to go from one energy state to another once it has "decided" to do so, then "garden variety" quantum mechanics is silent. You might use the Heisenberg uncertainty principle in the form dE*dt ~ h where dE is the energy difference, dt is the transition time, and 'h' is Planck's constant, but this is really a cop-out to avoid the very difficult question of: "How does the electron behave with the surrounding electric and magnetic fields "as it moves" from one state to another???" This becomes really tricky, and not really settled to my knowledge, because what you are asking is: "What is happening to the wave function's dynamical behavior?" This question is about: "What is a wave function? What is quantum mechanics? What is a photon of electromagnetic radiation?" These questions are not settled.

If you want to delve into these questions, I recommend that you read "Schrdinger's Kittens and the Search for Reality: Solving the Quantum Mysteries" by John Gribbon. It is readable and he lays bare some really fundamental questions that relate to your question.

Vince Calder

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