The following quantum numbers are possible for how many orbital? n=3, l=2, m=+2 (a) 1 (b) 2 (c)

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The following quantum numbers are possible for how many...

Key Concepts

Principal Quantum Number

The principal quantum number (n) indicates the overall energy level and size of an orbital in an atom. It is a positive integer where larger values of n correspond to orbitals that are further from the nucleus and have higher energy. In quantum mechanics, n is essential for determining the radial distribution of electrons and organizing the electron configuration in atoms.

Azimuthal Quantum Number

The azimuthal quantum number (l) defines the shape of the orbital and is an integer that ranges from 0 to n-1. It determines the orbital angular momentum, which affects the orbital’s angular shape. For example, l = 0 corresponds to s orbitals, l = 1 to p orbitals, and l = 2 to d orbitals, each having distinct geometries.

Magnetic Quantum Number

The magnetic quantum number (m) specifies the orientation of the orbital in space relative to an external magnetic field. Its values range from -l to +l, including zero. This quantum number further divides orbitals within the same subshell into distinct orientations and is crucial for understanding the spatial distribution of electrons.

Atomic Orbital

An atomic orbital is a region of space around the nucleus where there is a high probability of finding an electron. The combination of quantum numbers (n, l, m) uniquely defines one specific orbital. In this context, the given set of quantum numbers (n=3, l=2, m=+2) designates one uniquely defined orbital.

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