Schroedinger Theory of One-Electron Atom

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What is the significance of the Schroedinger theory of the one-electron atom?

It forms the foundation of the quantum mechanical treatment of all multielectron atoms, molecules, and nuclei.

What complicates the treatment of the one-electron atom compared to one-dimensional systems?

Its three-dimensional nature and the presence of two particles.

Why is the one-electron atom considered the simplest bound system in nature?

Because it consists of only a positively charged nucleus and a negatively charged electron.

How does the three-dimensional character of the one-electron atom affect mathematical procedures?

It complicates the mathematical procedures but they are straightforward extensions of simpler ones used in one-dimensional systems. Signup and view all the answers

Why do quantum mechanical phenomena involving angular momentum arise in the one-electron atom?

Due to its three-dimensional character and the presence of two particles. Signup and view all the answers

What are the two main components of the one-electron atom?

A positively charged nucleus and a negatively charged electron. Signup and view all the answers

What is the significance of nodal surfaces in the context of one-electron atoms?

Nodal surfaces represent regions within the atom where the probability of finding an electron is zero. Signup and view all the answers

How does the probability density function near the nucleus depend on the quantum number l?

The probability density near the nucleus increases as the quantum number l increases. Signup and view all the answers

What is the role of orbital angular momentum in quantum physics?

Orbital angular momentum plays a key role in determining the energy levels and spatial distribution of electrons in atoms. Signup and view all the answers

Explain the concept of eigenvalues in the context of one-electron atoms.

Eigenvalues represent the possible energy levels that an electron can occupy in the atom. Signup and view all the answers

How do the eigenfunctions of a one-electron atom compare in the Bohr and Schrödinger treatments?

The Schrödinger treatment provides a more accurate description of the electron's behavior compared to the Bohr model. Signup and view all the answers

What is the radial probability density in the context of one-electron atoms?

Radial probability density describes the likelihood of finding an electron at a certain distance from the nucleus. Signup and view all the answers

How many possible values of l are there for each value of n in an isolated one-electron atom?

n Signup and view all the answers

How many possible values of m1 are there for each value of l in an isolated one-electron atom?

(2l + 1) Signup and view all the answers

How many degenerate eigenfunctions are there for each value of n in an isolated one-electron atom?

n^2 Signup and view all the answers

What does the table in the text show about the possible values of quantum numbers for n = 1, 2, and 3?

Possible values of quantum numbers Signup and view all the answers

What phenomenon removes the degeneracy with respect to r in the potential for alkali atoms?

Change in the r dependence of the potential Signup and view all the answers

What is the main difference between the mathematical techniques used in obtaining eigenvalues in quantum mechanics and the ones used in the Bohr model?

Complexity Signup and view all the answers