Schroedinger Theory of One-Electron Atom
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Questions and Answers

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?

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

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

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

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

<p>A positively charged nucleus and a negatively charged electron.</p> Signup and view all the answers

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

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

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

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

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

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

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

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

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

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

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

<p>Radial probability density describes the likelihood of finding an electron at a certain distance from the nucleus.</p> 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?

<p>n</p> 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?

<p>(2l + 1)</p> Signup and view all the answers

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

<p>n^2</p> 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?

<p>Possible values of quantum numbers</p> Signup and view all the answers

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

<p>Change in the r dependence of the potential</p> 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?

<p>Complexity</p> Signup and view all the answers

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