consider the 7p(z) orbital. a0 list the quantum numbers for an electron in this state. b) list all degenerate orbitals for an electron in this state. c) how many radial nodes does this orbital have? d) how many angular nodes does this orbital have? e) write the complete hydrogen wavefunction for this orbital. f) sketch the radial wavefunction for this orbital.

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Lelia LubowitzLv2

29 Sep 2019

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Consider the 4pz orbital for the hydrogen atom (Z=1).

a) The radial portion of the wave function for this orbital is listed below:

R(r) = [(1/ao)^3/2/ (0.0645) ] [( 5-5p+p^2]p(e-p) p= (2 Z /n(ao))r
n=principle quantum number
**How many radial nodes does this orbital have?
b)What are the values of r for the radial node(s)? Express r in both units of ao and angstroms.

**a) n-l-1=4-1-1=2... Therefore, I understand that there are 2 radial nodes for part a. I just need help with part b mostly. I got stuck in the math towards the end.

(a) With reference to Figure 6.19, what is the relationship between the number of nodes in an s orbital and the value of the principal quantum number? (b) Identify the number of nodes; that is, identify places where the electron density is zero, in the 2p_x orbital; in the 3s orbital. (c) What information is obtained from the radial probability functions in Figure 6.19? (d) For the hydrogen atom, list the following orbitals in order of increasing energy: 3s, 2s, 2p, 5s, 4d.