Question

Which of the following set-builder notations correctly represents the set (−2,−1,0,1,2,…)?

(a) (x ∈ Z | −2 ≤ x ≤ 2)
(b) (x ∈ Z | x < 0)
(c) (x ∈ Z | x ≥ 0)
(d) (x ∈ Z | −2 < x < 2)

Answer 1

The allowed spectroscopic notations that follow the rules of quantum numbers are a. 1s¹, c. 4s², and d. 3p², as they correspond to valid combinations of principal (n) and angular momentum (l) quantum numbers. Options b and e are incorrect due to invalid combinations of quantum numbers for respective shells and subshells.

Step-by-step explanation:

The question pertains to which of the given spectroscopic notations is allowed according to the quantum number rules. Each electron in an atom is described by four quantum numbers: the principal quantum number (n), angular momentum quantum number (l), magnetic quantum number (ml), and spin quantum number (ms). The principal quantum number can be any positive integer starting from 1. The angular momentum quantum number can be any integer from 0 to n-1. The magnetic quantum number can range from -l to l, and the spin quantum number can be either -1/2 or 1/2.

Therefore, the correct spectroscopic notations that do not violate the quantum number rules are a. 1s¹, c. 4s², and d. 3p².