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Chapter 4: Problem 160

Which subshell has the lowest energy? (a) \(4 s\) (b) \(3 p\) (c) \(2 p\) (d) \(3 s\) (e) \(2 s\)

Short Answer

Expert verified
The subshell with the lowest energy is (e) \(2s\).

Step by step solution

01

List the given subshells and their quantum numbers

: First, let's list the given subshells and their corresponding quantum numbers (n, l): (a) \(4s: n = 4, l = 0\) (s corresponds to l = 0) (b) \(3p: n = 3, l = 1\) (p corresponds to l = 1) (c) \(2p: n = 2, l = 1\) (d) \(3s: n = 3, l = 0\) (e) \(2s: n = 2, l = 0\)
02

Calculate the (n + l) values for each subshell

: Now, calculate the (n + l) values for each subshell: (a) \(4s: n + l = 4 + 0 = 4\) (b) \(3p: n + l = 3 + 1 = 4\) (c) \(2p: n + l = 2 + 1 = 3\) (d) \(3s: n + l = 3 + 0 = 3\) (e) \(2s: n + l = 2 + 0 = 2\)
03

Identify the subshell with the lowest (n + l) value

: Among the given subshells, the one with the lowest (n + l) value is: (e) \(2s: n + l = 2\)
04

Check for any subshells with the same (n + l) value

: There are no other subshells with the same (n + l) value as the \(2s\) subshell. Therefore, there's no need to compare their n values.
05

Write the answer

: The subshell with the lowest energy is: (e) \(2s\)

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