# Energy Level Transitions, transition time for e- to change energy states in atom

Gold Member
Given a simple atom like the Bohr atom (and possibly generalized to any other atom), I know that an electron can transition from one energy level to another, either by absorbing or releasing a photon of a precise hf. How much time does an electron take to make a transition from one energy level to another? I know the electron cannot be found physically in the space between energy levels. Does anyone know where such calculations can be found? Usually, the effect is considered "instantaneous" but I am curious as to the actual times of transition between energy levels.

Note: I didn't underline anything. I don't know why that spontaneously appears in my text.

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Bill_K
A transition from level A to level B will have a definite lifetime τ. As time goes on, the probability of finding the electron in level B will increase slowly to one, and correspondingly the probability of finding it still in level A will decrease smoothly to zero. By the time a lifetime or two has elapsed, the electron is very likely to have decayed.

Nevertheless, at any given time the electron is either entirely in A or entirely in B. It has either decayed or not decayed. You cannot catch it halfway! In this sense the actual transition takes no time at all - it is instantaneous.

Drakkith
Staff Emeritus
Bill, you are saying that an excited electron has a chance to fall to a lower energy level in a certain amount of time, leading to a "half-life"?

Bill_K
Yes, excited QM states all follow the same law of exponential decay, whether they be atomic, nuclear or what have you. The halflife of atomic transitions is normally very short. Exceptions to this are metastable states, e.g. states with high orbital angular momentum, whose decays produce "forbidden" spectral lines. Quoting Wikipedia, "so-called meta-stable states usually have lifetimes of order milliseconds to seconds, compared to less than a microsecond for decay via permitted transitions."

Forbidden lines are most frequently observed in interstellar clouds, where high vacuum gives the atoms ample time to decay without bumping into something.

Gold Member
Wow, microseconds. That was the time scale I was looking for. Is that a typical transition time for most energy levels? I'd like to read more about this, but couldn't find a good website. If anyone knows of one, it'd be great to know.

Drakkith
Staff Emeritus
You realize that the transition itself is instantaneous Albert? It's only the time before the transition that is subject to the half-life.

Gold Member
I think we're getting to the heart of what I'm confused about. There appears to be two time intervals under discussion here.

Start with e- in ground state. It absorbs the photon and jumps to the higher energy state. The time interval I wanted to know about is how long the e- takes to disappear from the ground state, and reappear in the excited state. I have been taught this is supposed to be instantaneous, but I am not so sure now.

The second time interval people seem to be discussing is that, the e-, now in the excited state, will be up there for a certain lifetime (or half-life). Once the half-life/lifetime expires, the e-disappears from the excited state, to reappear in the ground state, emitting the photon.

So, I was asking about the time intervals of the e- making the transition between energy states, and not the time interval in which the e- spends in the new energy state itself. I couldn't find anything on the web after an exhaustive search, so maybe because there is nothing to answer my question about.

And, yes, since half-life is an average measurement, the average transition time will also do for energy states, I am just looking for something ball park.

Drakkith
Staff Emeritus
I believe the transition itself is instant.

tiny-tim
Homework Helper
i'm not a quantum sceptic, but i am a quantum cynic

it seems to me that if you can't detect something, or make any measurement of it, then quantum theory by definition says that it doesn't exist

there is no way of making any measurement of the electron "in transition"

nor can we make a measurement of the "before" and "after" states, and find that there is a time period in the middle in which that measurement cannot be made (thereby indicating a third state) …
our measurement will at all times give a result consistent with either the "before" or the "after" state!

(btw, as a matter of interest, which words got underlined on your screen? i saw nothing underlined )

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The time of transition can be calculated.It is inverse of the transition probability.The required calculation are given in Gordon baym 'Lectures on quantum mechanics' and also in greiner 'special chapters'

Bill_K