Q: Identify all that is incorrect about the set of four quantum numbers and explain why. {-3, 2, 1, 1/2}
A. -3 because there can't be a negative orbital.
Q: Identify all that is incorrect about the set of four quantum numbers and explain why. { 3, 2, 1/2, 1/2}
A. m(l) = 1/2 because you can't have halves.
A poorly written question. -3 is correctly identified; however, since that is not correct we don't know what else might be wrong since the first quantum number is wrong. But the question implies, at least, that there are others errors.
#2 is ok but you need to say m(l) = 1/2 because you can't have halves FOR m(l). [Note: you can have halves for m(s)]
In the first set of quantum numbers, {-3, 2, 1, 1/2}, the incorrect part is the value -3 for the principal quantum number (n). The principal quantum number represents the energy level of an electron in an atom. It can only take positive integer values (1, 2, 3...), indicating the different electron shells around the nucleus. Negative values are not possible for the principal quantum number since it represents the energy level and energy cannot be negative in quantum mechanics.
In the second set of quantum numbers, {3, 2, 1/2, 1/2}, the incorrect part is the value 1/2 for the magnetic quantum number (m(l)). The magnetic quantum number represents the orientation of the orbital in a specific electron shell around the nucleus. It can have integer values ranging from -l to +l, where l is the azimuthal quantum number. The azimuthal quantum number (l) corresponds to different subshells within an electron shell. In this case, the value of l is 2, so the possible values for m(l) should be -2, -1, 0, 1, and 2. Having halves (1/2) is not allowed for the magnetic quantum number because it must be an integer value.