Expectation values of the electron.

[hhhmortal]

Homework Statement

The expectation value <r> of the electron-nucleus separation distance 'r' is:

<r> = ʃ r |ψ|² dV.

(a) Determine <r> for the 1, 0, 0 state of hydrogen.

The Attempt at a Solution

Right, I've obtained the value for ψ = (1/πa³)^1/2 exp(-r/a)

I then replace dv by 4πr² dr.

I then put all of that in the equation above and try to integrate but I can't seem to go any further from here. Any help?

Thanks very much.

 

[Gokul43201]

Are you having trouble with the integral? Remember how to integrate by parts?

 

[hhhmortal]

I think it might be the integral. The problem is, I have an exponential term in the integral which I can't solve by parts? if so how?

 

[Gokul43201]

How are you trying to integrate, and what's the problem? Show us what you are doing.

 

[Brian_C]

Your integral should be of the form:

u dv = exp(-2r/a) r^3 dr

All you have to do is assign u and v. Hint: you will have to integrate by parts several times.