Determining Ground State Configuration in 2D Square Well with Aufbau Process

In summary, the Aufbau process can be used to determine the ground state electronic configuration for a 2D square well with 4 electrons. The multiplicity of the ground state electronic configuration is 2 due to the 2 degenerate states nx=1, ny=2 or nx=2, ny=1. The energy of this system is determined by the rules of filling for the particle in a box model, where the ground state can hold 2 electrons and the next energy level can hold 4 electrons. The system is diamagnetic, as predicted by the Aufbau principle.
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Homework Statement


use the Aufbau process to determine the ground state electronic configuration for the 2D sqare well if it contains 4 electrons. what is the multiplicity of the ground state electronic configuration? what is the energy of this 2 D 4 electrons system? and is the system diamagnetic or paramagnetic?

Homework Equations



the questions posted above are the second part of the questions, in the first part, the answer tells me that it is a 2D box with 2 degeneracy states nx=1, ny=2 or nx=2, ny=1.

The Attempt at a Solution


2 denerate state means multiplicity of 2? i have no idea of the other questions tho, how do you draw electronic configuration from particle in a box model? plus i thought particle in a box model only predicts pi bonds because they are delocalised? so should the ground state configuration exclude s orbitals and starts with p?
 
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Related to Determining Ground State Configuration in 2D Square Well with Aufbau Process

1. What is a particle in a 2D box question?

A particle in a 2D box question is a common physics problem that involves studying the behavior of a particle confined to a two-dimensional square or rectangular box. It is often used as an introductory example in quantum mechanics courses.

2. How is the particle in a 2D box problem solved?

The particle in a 2D box problem is typically solved using mathematical techniques such as separation of variables and boundary conditions. The resulting solution is a wavefunction that describes the probability distribution of the particle within the box.

3. What are the applications of the particle in a 2D box problem?

The particle in a 2D box problem has various applications in different fields of physics, including quantum mechanics, statistical mechanics, and solid state physics. It is also used in understanding the behavior of electrons in nanoscale structures and quantum dots.

4. How does the size of the box affect the particle's behavior?

The size of the box has a significant impact on the particle's behavior. As the box size increases, the energy levels of the particle increase, leading to a higher probability of finding the particle at the edges of the box. Conversely, a smaller box leads to lower energy levels and a higher probability of finding the particle at the center of the box.

5. What is the significance of the particle in a 2D box problem in quantum mechanics?

The particle in a 2D box problem is a fundamental example in quantum mechanics that helps in understanding the behavior of particles in confined spaces. It allows us to explore the concepts of energy quantization and wave-particle duality, which are essential in understanding the behavior of matter at a microscopic level.

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