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### Topic: Quantum Mechanics - The Uncertainty Principle  (Read 8346 times)

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#### soaring206

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##### Quantum Mechanics - The Uncertainty Principle
« on: February 14, 2005, 01:43:18 PM »
Okay, I'm trying to do a problem involving Heisenberg's uncertainty principle (?x * ?px ? ?/2), and I know what the answer is, but I can't figure out how to get the answer from what's been given to me.  This is the problem:

Though not strictly equivalent, there is a similar uncertainty relationship between the observables time and energy:
?E * ?t ? ?/2
In emission spectroscopy, the width of the lines (which gives a measure of ?E) in a spectrum can be related to the lifetime (that is, ?t) of the excited state.  If the width of a spectral line of a certain electronic transition is 1.00 cm-1, what is the minimum uncertainty in the lifetime of the transition?

Now, I know that ? = h/2?, and if the equation is rearranged to solve for ?t, it becomes ?t ? h/4??E (where h = Planck's constant (6.626x10-34 J*s)), but when I plug in all my numbers (6.626x10-34 J*s/4*3.14*1.00 cm-1), the units don't work out to give me seconds for ?t, and I don't come up with the book's answer of ?t ? 2.65x10-12 s.  Could someone please point me in the right direction with this?  Thank you!

#### Mitch

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##### Re:Quantum Mechanics - The Uncertainty Principle
« Reply #1 on: February 14, 2005, 02:35:36 PM »
You need to convert 1.00cm-1 to units of Joules.
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#### soaring206

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##### Re:Quantum Mechanics - The Uncertainty Principle
« Reply #2 on: February 14, 2005, 02:43:45 PM »
Ah ha...it's always the dumb little things that get me.  Thank you very much!