Final answer:
The first element that can have an electron with the set of quantum numbers (2, 1, 0, -1/2) is in the 2p subshell. The quantum numbers (5, 0, 0, +1/2) and (4, 2, -1, -1/2) are not allowed. The set of quantum numbers (3, 1, 1, +1/2) represents an electron in the 3p subshell.
Step-by-step explanation:
a. The set of quantum numbers (2, 1, 0, -1/2) represents an electron in the 2p subshell. In this subshell, the principal quantum number (n) is 2, the azimuthal quantum number (l) is 1, the magnetic quantum number (m) is 0, and the spin quantum number (ms) is -1/2.
b. The set of quantum numbers (5, 0, 0, +1/2) is not allowed because the azimuthal quantum number (l) must be less than the principal quantum number (n). In this case, l is equal to 0, which is not less than 5.
c. The set of quantum numbers (4, 2, -1, -1/2) is not allowed because the azimuthal quantum number (l) cannot be negative. In this case, l is equal to -1, which is not a valid value.
d. The set of quantum numbers (3, 1, 1, +1/2) represents an electron in the 3p subshell. In this subshell, the principal quantum number (n) is 3, the azimuthal quantum number (l) is 1, the magnetic quantum number (m) is 1, and the spin quantum number (ms) is +1/2.