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Calculating avg distance from nucleus 
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#1
Oct1509, 11:55 PM

P: 195

1. The problem statement, all variables and given/known data
Calculate the avg. distance from the Hydrogen nucleus for an electron in 2p. 2. Relevant equations <r> = int[r^3 R^2]dr from 0>infinity For Hydrogen 2p, R = (1/a)^3/2 (1/(2*sqrt(sigma))*sigma*exp(sigma/2) where sigma = r/a 3. The attempt at a solution I get 1/4a^4 (24 a^5) = 6a but the answer's supposed to be 5a. (5a for 2p is supposed to be less than 6a, which is the avg distance for 2s.) What am I doing wrong?????? 


#2
Oct1609, 12:35 AM

HW Helper
P: 5,003

[tex]\langle r\rangle=\int_{\text{all space}}r\psi(\textbf{r})^2d^3\textbf{r}=\int_0^{\infty}\int_0^{\pi}\i nt_0^{2\pi}\psi(\textbf{r})^2r^3\sin\theta dr d\theta d\phi[/tex] 


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