Enumerate the microstates of p3

Enumerate the microstates of p3. Determine the MS and ML values for each microstate.

The correct answer and explanation is :

To answer this question, let’s start by defining the important terms and understanding the concepts behind the enumeration of microstates.

Definitions:

1. Microstates: A microstate refers to a specific arrangement or configuration of quantum numbers (or other variables like spin) in a system. For an atom, a microstate represents a specific set of quantum numbers for electrons in the atom.
2. p3: This refers to the atomic orbital in which there are 3 electrons. The p orbital can hold a maximum of 6 electrons, with 3 electrons in the case of p3.
3. MS (Total Spin Quantum Number): The total spin quantum number (MS) is determined by the sum of the spin quantum numbers of the individual electrons. For each electron, the spin quantum number (ms) can be +1/2 or -1/2. The total spin quantum number is the sum of these individual spins.
4. ML (Magnetic Quantum Number): The magnetic quantum number (ML) specifies the orientation of the orbital in space. For a p orbital (which corresponds to an angular momentum quantum number l = 1), the possible values of ML are -1, 0, and +1.

Enumeration of Microstates for p3:

In the p3 configuration, there are 3 electrons distributed among the three p orbitals. Each electron can have different spin orientations and magnetic quantum numbers.

1. Electrons and Orbitals: The three electrons are placed in three p orbitals, corresponding to the magnetic quantum numbers ML = -1, 0, and +1.
2. Spin States: For each of these orbitals, the electron can have a spin quantum number ms = +1/2 or ms = -1/2. Thus, each orbital can hold an electron with spin +1/2 or -1/2.

Microstate Enumeration:

Each electron can be placed in one of the three orbitals (corresponding to ML = -1, 0, and +1). The spin states of the electrons are also considered, and we can have the following configurations:

1. All three electrons with parallel spins: All electrons have the same spin quantum number (either all +1/2 or all -1/2).
2. Two electrons with parallel spins and one with an opposite spin: Two electrons share the same spin, and the third one has the opposite spin.
3. All three electrons with different spins: This configuration is impossible for p3 since there are only two possible spin values per electron (either +1/2 or -1/2).

MS and ML values:

• MS (Total Spin Quantum Number): The value of MS is determined by the total spin of the system:
• For a configuration with all electrons having the same spin (all +1/2 or all -1/2), MS = +3/2 or MS = -3/2.
• For a configuration with two electrons having the same spin and one with the opposite spin, MS = +1/2 or MS = -1/2.
• ML (Magnetic Quantum Number): The total value of ML is the sum of the individual ML values for each electron:
• The ML values for each electron in the p3 configuration are -1, 0, and +1.
• The total ML value will always be 0 (i.e., -1 + 0 + 1 = 0).

Conclusion:

For p3, the possible microstates correspond to the various combinations of spin and magnetic quantum numbers. The total ML for all microstates will always be 0, but the total MS can vary depending on the spin configuration. The possible MS values are +3/2, +1/2, -1/2, and -3/2.