[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?

[Borek]

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

More likely e^-sigma/3

[allanf]

2. What exactly does the value of R_3p represent?

When writing the wavefunction for a hydrogen atom using spherical coordinates you can break the wave function into two main parts: the angular part and the radial part.  R_3p is the part of the wavefunction that depends only on the distance from the nucleus.  This is the part of the wavefunction where nodes show up.

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

Since you are looking for nodes, you are looking for the distance out from the center where the probability density is zero, not the wavefunction.

[Yggdrasil]

2. What exactly does the value of R_3p represent?

When writing the wavefunction for a hydrogen atom using spherical coordinates you can break the wave function into two main parts: the angular part and the radial part.  R_3p is the part of the wavefunction that depends only on the distance from the nucleus.  This is the part of the wavefunction where nodes show up.

Nodes can also show up in the angular wave function.  For example, for the p_z orbital, the xy-plane is a node.

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

Since you are looking for nodes, you are looking for the distance out from the center where the probability density is zero, not the wavefunction.

Since the probability density = |?|², setting the wavefunction equal to zero is equivalent to setting the probability density to zero.  But it is important that you realize that a node is defined as having zero probability of finding an electron at that radius, and not as the wavefunction having zero amplidute at that radius.