(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

This is the first question from a past exam paper I'm doing at the moment, and I'm not sure if it's a case that I'm doing something stupid, or if there is a problem with the question.

Q: The wavefunction of a deuteron can be approximated by:

[tex] \psi (r) = \frac{C}{r} e^{-\alpha r} [/tex]

Where [itex] \alpha = 0.23 fm^{-1}[/itex]Calculate the Normalisation Constant, C.

What is the probability that the separation of the two nucleons in the deuteron exceeds 2 fm, and what is their average separation.

3. The attempt at a solution

To work out C, I did:

[tex] \psi^{*}(r) = \frac{C}{r}e^{-\alpha r} [/tex]

[tex] C^2 \int^{\infty}_{0} r^{-2} e^{-2 \alpha r} = 1 [/tex]

But if you work out this integral, it diverges, so what now?

As for the other part(s), am I right in thinking that you do something along the lines of:

[tex] P(r>2fm) = \int^{\infty}_{2*10^{-15}} \psi(r) \psi^{*}(r) dr [/tex]

and

[tex] <r> = \int^{\infty}_{0} \psi(r) r \psi^{*}(r) dr [/itex]

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# Homework Help: Deuteron Wavefunction Question

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