Question

What are the possible values for the quantum numbers $n, \ell$, and $m_{\ell}$ ?

   What are the possible values for the quantum numbers $n, \ell$, and $m_{\ell}$ ?

Chemistry

Steven S. Zumdahl,… 7th Edition

Chapter 7, Problem 57

Instant Answer

Solved by Expert James Irizarry

10/19/2019

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The principal quantum number (n) can have any positive integer value (n = 1, 2, 3, ...). It determines the energy level and size of the electron's orbit. Show more…

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What are the possible values for the quantum numbers $n, \ell$, and $m_{\ell}$ ?

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Key Concepts

Principal Quantum Number (n)

This number defines the energy level or shell of an electron in an atom and determines the most probable distance of the electron from the nucleus. It is a positive integer (n = 1, 2, 3, ...) and is fundamental in establishing the electron's energy level in quantum mechanics.

Orbital Angular Momentum Quantum Number (?)

This quantum number relates to the shape of the electron's orbital and describes the orbital angular momentum. It can take on integer values ranging from 0 to n-1 for each principal quantum number n, thereby linking the allowed orbital shapes to the energy level of the electron.

Magnetic Quantum Number (m?)

This quantum number determines the orientation of the electron's orbital angular momentum in space relative to a chosen axis. It can take on integer values from -? to +?, including 0, which specifies the degeneracy of orbitals in a given subshell.

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