The quantum numbers of the differentiating (last) electron of a neutral atom in its ground state are n = 3 , l = 1 , m_l = -1 , and m_s = + 1 2 . Assuming that the orbitals of a subshell are filled in the order of increasing m_l (i.e., -1, 0, +1 ), the atomic number of the element is:

Step-by-step solution

The principal quantum number n = 3 and azimuthal quantum number l = 1 correspond to the 3p subshell. The magnetic quantum number m_l = -1 and spin quantum number m_s = + 1 2 represent the first electron entering the 3p subshell, assuming filling starts from the lowest m_l value. Thus, the differentiating electron is in the 3p^1 configuration. The complete electronic configuration of the atom is 1s^2 2s^2 2p^6 3s^2 3p^1 . The atomic number is the total number of electrons in the neutral atom: 2 + 2 + 6 + 2 + 1 = 13