The principal quantum number (n):
(1) specifies the subshell of the orbital.
(2) specifies the principal shell of the orbital.
(3) specifies the 3-D shape of the orbital.
(4) specifies the maximum number of electrons.
(5) none of the above
The correct answer is (2) specifies the principal shell of the orbital.
To arrive at this conclusion, you can refer to the definition of the principal quantum number. In quantum mechanics, the principal quantum number (n) is one of the four quantum numbers that describe the unique energy levels (or shells) within an atom, specifically, the energy levels of electrons in an atom's electron cloud.
The principal quantum number (n) determines the energy level or shell in which an electron is located. The value of n can be any positive integer starting from 1. Each value of n corresponds to a specific energy level, with n=1 being the lowest energy level closest to the nucleus.
The other answer choices do not accurately describe the principal quantum number:
(1) specifies the subshell, but the correct term for this is the azimuthal quantum number (l).
(3) specifies the shape of the orbital, but this is described by the azimuthal quantum number as well as the magnetic quantum number.
(4) specifies the maximum number of electrons, but this is described by the Pauli exclusion principle and the rules for filling electron orbitals.
Thus, the correct answer is (2) the principal quantum number (n) specifies the principal shell of the orbital.