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Chapter 8: Problem 52

For \(n=1,\) write all the possible sets of quantum numbers \(\left(n, l, m, m_{s}\right)\).

Short Answer

Expert verified
The two possible sets of quantum numbers for \(n=1\) are \(\left(1, 0, 0, +\frac{1}{2}\right)\) and \(\left(1, 0, 0, -\frac{1}{2}\right)\).

Step by step solution

01

Determine the possible values of l

Referring to rule 1, the value of l ranges from 0 to n-1. Since n=1, there is only one possible value for l: \(l = 0\)
02

Determine the possible values of m

Referring to rule 2, the value of m ranges from -l to +l. Since l=0, there is only one possible value for m: \(m = 0\)
03

Determine the possible values of m_s

Referring to rule 3, there are two possible values for m_s: +1/2 and -1/2. Therefore, the possible values for m_s are: \(m_s = +\frac{1}{2}\) and \(m_s = -\frac{1}{2}\)
04

List all possible sets of quantum numbers

Now, we can combine all possible quantum numbers for n=1: Set 1: \( (1,0,0,+\frac{1}{2})\) Set 2: \( (1,0,0,-\frac{1}{2})\) There are two possible sets of quantum numbers for n=1: \[\left(1, 0, 0, +\frac{1}{2}\right) \text{ and } \left(1, 0, 0, -\frac{1}{2}\right)\]

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