Homework Statement
Determine the point group of the chair conformer of cyclohexane. How many Raman active vibrations and how many infrared active vibrations might you expect to detect in its spectrum?
Homework Equations
(see link below)
The Attempt at a Solution...
Yeah, i realized i hadnt evaluated the final integral. When i did i got that result and substituting the limits gave me that answer. Thanks for your help!
I have hosted an image of my calculations in word (LaTex still isn't working for me):
http://img221.imageshack.us/img221/8241/probof1selectron.jpg
Are my workings right?
When I substitute in the limts, I get negative numbers which I am sure is not right.
Thanks again.
Sorry, i really can't use Latex. I did it in word and this is the best i can do:
P= ∫▒4/(a_0^3 ) r^2 e^((-2r)/a_0 ) dr
P= ∫▒4/(a_0^3 ) 〖a_0〗^2 r^2 e^(-2x ) a_0 dx
P= ∫▒〖4x〗^2 e^(-2x) dx
P=4∫▒x^2 e^(-2x) dx
P= -1/2 x^2 e^(-2x)+∫▒〖xe^(-2x) 〗 dx
P= -1/2 x^2 e^(-2x)+xe^(-2x) ∫▒1/2...
Homework Statement
Given that the probability of finding a 1s electron in a region between r and r + dr is:
P = \frac{4}{a_{0}^{3}}r^{2}e-2r/a0dr
work out the probability that an electron would be found within a sphere of radius:
i) a0
Homework Equations
The Attempt at a...
Im not entirely sure I understand what you're asking but acidity increases down a group because the bond between the conjugate base and the hydrogen gets weaker. Think of it in terms of orbital overlap. HF should be a stronger acid than HI because F is the most electronegative atom but the...
Oh i see so when the second a+ operates, the factor becomes \sqrt{n+2} and not \sqrt{n+1}.\sqrt{n+1} = n+1 (it is not multiplied but instead increases the number that is added to n).
<n|n+1> would give an answer of zero therefore making the entire Dirac bra-ket and the factors zero?
This...
I have solved the question you gave and got n^1/2.n+1<n|n+1>. (Sorry if this is wrong but I am trying!)
Thinking about it, after expanding and solving all the terms (aaa + a+a+a - ...), it should cancel to zero?
Firstly, thank you for the reply.
Secondly, does that mean, being orthonormal, <n'|n> = 0?
The kind of terms? All i can think is that they are operators and operate on n to raise or lower is as such:
a|n> = n^1/2|n-1>
a+|n> = (n+1)^1/2|n+1>
The expansion? By expanding the bracket...
Be careful how you label your species here. OH- can be seen as a base (and a nucleophile) but H2O is not the conjugate acid in the sense that you mean, H3O+ would be the 'acid'. This is because (using your HCl equation) HCl does not simply become two separate ions in solution. The acid will...
1. Explain why <n|(a-a+)^3|n> must be zero
2. a and a+ (a dagger) are the raising and lowering operators (creation and annihilation operators).
3. Because it says explain, I am not sure any mathematical proof is needed. I am best answer is that because (ignoring that the bracket...