Final answer:
The pair (1,3) is not a possible combination of quantum numbers in atomic physics because the orbital angular quantum number must be less than the principal quantum number. Thus, since 3 is greater than (n-1) when n is 1, the answer is that this is impossible and never happens.
Step-by-step explanation:
The pair (1,3) represents possible values of quantum numbers in physics, specifically those that describe atomic orbitals. The question whether (1,3)∈n×n (where 'n' stands for the principal quantum number and the cross signifies a Cartesian product) depends on the rules governing quantum numbers in atoms. According to the rules of quantum mechanics, the orbital angular quantum number ('l') can range from 0 to (n-1), where 'n' is the principal quantum number. Therefore, if n equals 1, the only possible value for l is 0, since l must always be less than n. This means that (1,3) is not a possible pair in the set n×n because 3 is not less than or equal to (n-1) when n is 1.
In summary, the proposed pair (1,3) does not comply with the rules for quantum numbers in atomic physics, making the option, "this is impossible! it never happens," the accurate response.