Final answer:
Quantum numbers describe an electron's state in an atom. For a 5p electron, the set of quantum numbers should include n=5, l=1, ml from -1 to 1, and ms being either +1/2 or -1/2. Incorrectly designated quantum numbers violate the rules and are not allowed.
Step-by-step explanation:
Quantum Numbers and Spectroscopic Notation
The quantum numbers of an electron describe its energy state within an atom. There are four quantum numbers: the principal quantum number (n), the azimuthal quantum number (l), the magnetic quantum number (ml), and the spin quantum number (ms).
For a 5p electron, the set of quantum numbers would be: n=5 (since it's the 5th energy level), l=1 (since p corresponds to l=1), ml can range from -l to l, therefore from -1 to 1, and ms can be either +1/2 or -1/2.
A spectroscopic notation that is not allowed would violate the rules for these quantum numbers, such as having a wrong l value for a given subshell, an ml value outside the allowed range, or an incorrect number of electrons. Examples of incorrect spectroscopic notations for a 5p electron might include a principal quantum number other than 5, an azimuthal quantum number other than 1, or a magnetic quantum number that is not an integer between -1 and 1.