Chemical Forums
Chemistry Forums for Students => Physical Chemistry Forum => Topic started by: soaring206 on February 14, 2005, 01:43:18 PM
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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!
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You need to convert 1.00cm-1 to units of Joules.
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Ah ha...it's always the dumb little things that get me. Thank you very much! :)