Determine whether each of the following sets of quantum numbers for the hydrogen atom is valid. If a set is not valid, then indicate which of the quantum numbers has a value that is not valid: e. n = 2, l = 2, ml = 1, ms = +1/2

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Quantum numbers describe the properties of atomic orbitals and the properties of electrons in orbitals.

The principal quantum number, n, can be any positive integer (n = 1, 2, 3, ...). It indicates the energy level and size of the orbital.

The azimuthal quantum number, l, can be any integer from 0 to n-1. It defines the shape of the orbital.

For n = 2, the possible values of l are 0 and 1. Therefore, l = 2 is not valid for n = 2.

Since l = 2 is not valid, the set of quantum numbers is not valid.

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Key Concepts

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Quantum Numbers

Quantum numbers are a set of four numbers that describe the unique quantum state of an electron in an atom. They include the principal quantum number (n), azimuthal quantum number (l), magnetic quantum number (ml), and spin quantum number (ms). Each quantum number has specific rules governing its possible values, which are essential for determining the electron's energy level and orbital shape.

Principal Quantum Number (n)

The principal quantum number (n) indicates the main energy level of an electron in an atom and can take positive integer values (1, 2, 3, ...). Higher values of n correspond to electrons that are further from the nucleus and have higher energy. In the given set, n = 2 is valid as it is a positive integer.

Azimuthal Quantum Number (l)

The azimuthal quantum number (l) defines the shape of the electron's orbital and can take integer values from 0 to (n-1). For n = 2, the possible values of l are 0 and 1, corresponding to the s and p orbitals, respectively. In the provided set, l = 2 is invalid because it exceeds the maximum allowed value for n = 2.

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