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### Topic: uncertainty principle??  (Read 2760 times)

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#### arlaness

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##### uncertainty principle??
« on: August 27, 2007, 07:56:24 AM »
i have a question from my tutorial which i do not understand at all... my lecturer gave no commnets on it either so i hope someone can help me with this.

2.A typical bond-length is 1 Å.  If we knew where electrons were in a bond or a “loan pair”, then you would expect that their position would be known to, say, 1% of a typical bond length.  (a) What, therefore, is the uncertainty in the position of an electron if we were able to quite accurately say where it was in a bond or loan-pair?  (b) Using the uncertainty principle, what is the corresponding uncertainty in the electrons momentum?  (c) Electrons in bonds don’t move as fast as 10% of the speed of light, but, as an upper limit to their speed, assume they do.  What momentum would an electron have if it moved at 10% of the speed of light in a bond or loan-pair?  (d) What is the percentage error in the momentum of the electron due to the uncertainty principle?  (e) What percentage error does this correspond to in the electron’s kinetic energy?  (f) A typical bond energy is 400 kJ mol-1.  What error would you place on this energy if you were able to say where the electron was in the bond to 1% of its bond length?

#### Yggdrasil

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##### Re: uncertainty principle??
« Reply #1 on: August 27, 2007, 05:50:52 PM »
Please read the Forum Rules.  They specify that you should show that you have at least tried to answer the problem first.

2.A typical bond-length is 1 Å.  If we knew where electrons were in a bond or a “loan pair”, then you would expect that their position would be known to, say, 1% of a typical bond length.  (a) What, therefore, is the uncertainty in the position of an electron if we were able to quite accurately say where it was in a bond or loan-pair?

If you know the position to 1% of a typical bond length (1 Å), what uncertainty does this correspond to?

Quote
(b) Using the uncertainty principle, what is the corresponding uncertainty in the electrons momentum?
Do you know the mathematical formualtion of the Heisenberg Uncertainty principle?  If not, look it up in your notes or in your chemistry text (alternatively, google it)

The rest are relatively easy calculations once you have the right numbers and constants.