Which of the following sets of quantum numbers are not...

Which of the following sets of quantum numbers are not allowed in the hydrogen atom? For the sets of quantum numbers that are incorrect, state what is wrong in each set.
a. $n=3, \ell=2, m_{\ell}=2$
b. $n=4, \ell=3, m_{\ell}=4$
c. $n=0, \ell=0, m_{\ell}=0$
d. $n=2, \ell=-1, m_{\ell}=1$

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Key Concepts

Azimuthal Quantum Number (l)

Also referred to as the orbital angular momentum quantum number, this number defines the shape of the electron's orbital. For a given principal quantum number n, the allowed values of l are integers from 0 to n-1. Any l value outside this range is disallowed. Additionally, l must be a non-negative integer; negative values are not permitted.

Magnetic Quantum Number (m?)

This quantum number specifies the orientation of the orbital in space relative to an external magnetic field. For a given azimuthal quantum number l, m? can take on integer values ranging from –l by increments of 1 up to +l. Values of m? outside of this range are not allowed, as they would imply an impossible orientation for the orbital.

Principal Quantum Number (n)

This quantum number represents the main energy level or shell of the electron in an atom. It must be a positive integer (n = 1, 2, 3, ...), as it sets the scale for the electron's energy and the size of its orbital. An n value of 0 is not allowed, as it would correspond to a non-existent energy level.

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