Calculate Value of r for Hydrogen Atom 3p Orbital Node

[endeavor]

"(a) Use the radial wave function for the 3p orbital of a hydrogen atom (see Table 15.2) to calculate the value of r for which a node exists.
(b) Find the values of r for which nodes exist for the 3s wave function of the hydrogen atom."

For part a, I looked at Table 15.2 and found the equation R_3p = 4/(81*square root of 6) * (Z/a₀)^(3/2) * (6*sigma - sigma²) exp (-sigma/3)
where sigma = Z*r/a₀ and a₀ = 0.529 * 10^-10m

1. Does exp (-sigma/3) mean raise (6*sigma - sigma²) to the (-sigma/3) power?

2. What exactly does the value of R_3p represent?

3. To solve this problem do I set R_3p to 0 and solve for r?

 

[siddharth]

First, if you need help with LaTeX, try https://www.physicsforums.com/showthread.php?t=8997&page=52".

1. Does exp (-sigma/3) mean raise (6*sigma - sigma2) to the (-sigma/3) power?

No. It means $$e^{-\sigma/3}$$. So you'd have $$(6\sigma - \sigma^2)(e^{-\sigma/3})$$

What exactly does the value of R3p represent?

While solving Schroedinger's equation with various approximations for the Hydrogen atom, you would have probably used the separation of variables technique, to separate the equation into a radial part, and an angular part.

R3p is a solution to the radial wave equation, for certain values of n,l which signify the 3p orbital.

To solve this problem do I set R3p to 0 and solve for r?

To find the nodes, you need to find where the probability of finding the electron is zero. So, how would you solve it? Can you take it from here?

 

[t!m]

To find the nodes, you need to find where the probability of finding the electron is zero. So, how would you solve it? Can you take it from here?

I'm not sure if you're trying to make him think about this in a broader picture, but a radial node is simply where the radial function is equal to 0, as the OP said. It is true that there is 0 probability of finding the electron at this radius, but I feel that is additional information.