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Chapter 8: Problem 56

For \(n=2,\) write all the possible sets of quantum numbers \(\left(n, l, m, m_{s}\right)\).

Short Answer

Expert verified
The possible sets of quantum numbers for \(n=2\) are: 1. (2, 0, 0, -1/2) 2. (2, 0, 0, +1/2) 3. (2, 1, -1, -1/2) 4. (2, 1, -1, +1/2) 5. (2, 1, 0, -1/2) 6. (2, 1, 0, +1/2) 7. (2, 1, 1, -1/2) 8. (2, 1, 1, +1/2)

Step by step solution

01

Find Possible Azimuthal Quantum Numbers (l)

Given n=2, the possible values for the azimuthal quantum number l are 0 and 1 (l can have values ranging from 0 to n-1).
02

Find Possible Magnetic Quantum Numbers (m) for each l value

For l=0, the magnetic quantum number m can only be 0 (ranging from -l to +l). For l=1, the magnetic quantum number m can be -1, 0, or 1.
03

Combine m with Spin Quantum Numbers (ms) for each l value

Now we will list all possible sets of quantum numbers for n=2, l=0: - For m=0, ms can be -1/2 or +1/2, so we have two sets: (2,0,0,-1/2) and (2,0,0,+1/2) Next, we will list all possible sets for n=2, l=1: - For m=-1, ms can be -1/2 or +1/2, so we have two sets: (2,1,-1,-1/2) and (2,1,-1,+1/2) - For m=0, ms can be -1/2 or +1/2, so we have two sets: (2,1,0,-1/2) and (2,1,0,+1/2) - For m=1, ms can be -1/2 or +1/2, so we have two sets: (2,1,1,-1/2) and (2,1,1,+1/2)
04

Combine All Possible Sets of Quantum Numbers

Finally, let's list all the possible sets of quantum numbers for n=2: 1. (2, 0, 0, -1/2) 2. (2, 0, 0, +1/2) 3. (2, 1, -1, -1/2) 4. (2, 1, -1, +1/2) 5. (2, 1, 0, -1/2) 6. (2, 1, 0, +1/2) 7. (2, 1, 1, -1/2) 8. (2, 1, 1, +1/2) These are all the possible sets of quantum numbers for an electron in the second energy level (n=2).

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Most popular questions from this chapter

Explain how a hydrogen atom in the ground state \((l=0) \quad\) can interact magnetically with an external magnetic field.

Find the minimum torque magnitude \(| \vec{\tau}\) | that acts on the orbital magnetic dipole of a \(3 p\) electron in an external magnetic field of \(2.50 \times 10^{-3} \mathrm{T}\)

List all the possible values of \(s\) and \(m_{s}\) for an electron. Are there particles for which these values are different?

(a) What is the minimum value of \(l\) for a subshell that contains 11 electrons? (b) If this subshell is in the \(n=5\) shell, what is the spectroscopic notation for this atom?

If an atom has an electron in the \(n=5\) state with \(m=3,\) what are the possible values of \(l ?\)
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