Final answer:
The correct option is d.
Subshells such as 1d and 3g do not exist because their angular momentum quantum numbers exceed the limit set by their principal quantum numbers. Subshells 4p, 4s, 4d, and 4f are all possible according to quantum mechanical rules, so none of the options given are incorrect.
Step-by-step explanation:
According to the rules governing the values of quantum numbers, the subshells that do not exist due to the constraints upon the angular momentum quantum number (l) are 1d, 2g, and any theoretical subshell with a higher angular momentum quantum number than is allowed for the given principal quantum number (n).
The principal quantum number n starts at 1, and the angular momentum quantum number l can be any whole number from 0 to n-1.
Therefore, notations such as 1d (since d corresponds to l=2 which is not possible for n=1), 3g (g corresponds to l=4, which is not possible for n=3), and the like are not possible and violate the rules. When considering the options given (a) 4p, (b) 4s, (c) 4d, and (e) 4f, all these subshells are possible, so the correct answer would be (d) None of the above.