Consider the following orbital in the n=5 shell:

This orbital has [Fill in the blank]
angular node(s) and [Fill in the blank]
radial node(s).
(Input numbers only.)

Question

Consider the following orbital in the n=5 shell:

This orbital has [Fill in the blank]
 angular node(s) and [Fill in the blank]
 radial node(s).
(Input numbers only.)

BlackTom AI · Accepted Answer

To analyze the orbital in the n=5 shell, start by recalling two key relationships in atomic orbitals:
- The total number of nodes for a given n is n - 1. Here, n = 5, so total nodes = 5 - 1 = 4.
- The total number of nodes equals the sum of angular nodes (l) and radial nodes (n_r): n - 1 = n_r + l.
Now we need the value of l for this particular orbital. The picture shows an f-type orbital, which corresponds to l = 3 (s:0, p:1, d:2, f:3).
Using n - 1 = n_r + l with n = 5 and l = 3: 4 = n_r + 3, so n_r = 1.
Therefore, the orbital has 3 angular nodes and 1 radial node.
Answering the two blanks in order:
- Angular node(s): 3
- Radial node(s): 1
This matches the given input values and satisfies the node-count relationship for n = 5, l = 3.

Notes on alternative possibilities: If one misidentified the orbital as an s, p, or d type, the angular node count would be wrong (s: 0, p: 1, d: 2), leading to inconsistent total nodes with n = 5. Remember the general formulas n_r = n - l - 1 and total nodes = n - 1 to verify consistency.

CHEM1012 (L2) Online Quiz #1

Consider the following orbital in the n=5 shell: This orbital has [Fill in the blank] angular node(s) and [Fill in the blank] radial node(s). (Input numbers only.)

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