[soaring206]

I'm having a lot of trouble with two of my homework problems tonight.  I have been completely through my textbook and all over the internet, but I can't find what I'm looking for anywhere.  I have no idea where to even begin on the following two problems, so if someone could just give me a push in the right direction (like an equation or something), I'd greatly appreciate it!

1. Calculate the root-mean-square (standard deviation) displacement of the nuclei of ¹²C¹⁶O in the ground state and compare it to the equilibrium bond length of 112.832 pm.  (HINT: <x>=0) Use ?=(k?/?²)^1/2 and k=1903 kg/s².

2. Calculate the value of <r> for the n=2, l=1, m_l=0 state and the n=2, l=0, m_l=0 state of the hydrogen atom.

Any help at all would be appreciated...thank you so much in advance!

[Mitch]

2. Do you know the wavefunction for that state?

[soaring206]

Unfortunately, no...that's all the information given to me in the question.

[Mitch]

Open your book. The wavefunctions are there.

[soaring206]

Oh, right...sorry.

n=2. l=1, m_l=0
1/8(2Z³/?a³)^1/2(Zr/a)e^-Zr/2acos?

n=2, l=0, m_l=0
1/8(2Z³/?a³)^1/2(2-Zr/a)e^-Zr/2a

a=4??₀?²/?e²

[Mitch]

Now just take the integral of (phi<r>phi*) and you'll be set.

[soaring206]

Hmm...thanks Mitch.  I feel dumb...can't believe I didn't realize that.  Lol.

Any ideas on the first one perchance?