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Chapter 7: Problem 155

Which of the following orbital designations are incorrect: \(1 s,\) $1 p, 7 d, 9 s, 3 f, 4 f, 2 d ?$

Short Answer

Expert verified
The incorrect orbital designations are 1p, 3f, and 2d, as they do not satisfy the condition \(l \leq n-1\).

Step by step solution

01

Analyze each orbital designation and compare it to the condition l ≤ (n-1)

For each orbital designation, we will write down the principal quantum number (n) and the azimuthal quantum number (l) to compare them to the given rule (l ≤ n−1). 1. 1s: n = 1, l=0 (for s) 2. 1p: n = 1, l=1 (for p) 3. 7d: n = 7, l=2 (for d) 4. 9s: n = 9, l=0 (for s) 5. 3f: n = 3, l=3 (for f) 6. 4f: n = 4, l=3 (for f) 7. 2d: n = 2, l=2 (for d) Now, we will compare each pair (n, l) to the condition l ≤ n−1.
02

Determine the incorrect designations by comparing each pair (n, l) to the condition l ≤ (n-1)

Let's analyze and compare each pair (n, l) to the condition l ≤ n−1: 1. 1s: l ≤ n−1 => 0 ≤ 0 (True) 2. 1p: l ≤ n−1 => 1 ≤ 0 (False) 3. 7d: l ≤ n−1 => 2 ≤ 6 (True) 4. 9s: l ≤ n−1 => 0 ≤ 8 (True) 5. 3f: l ≤ n−1 => 3 ≤ 2 (False) 6. 4f: l ≤ n−1 => 3 ≤ 3 (True) 7. 2d: l ≤ n−1 => 2 ≤ 1 (False)
03

Conclusion

Based on the analysis in Step 2, we can conclude that the incorrect orbital designations are 1p, 3f, and 2d.

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