Final answer:
The set of quantum numbers {1, 0, 0, 1/2} is valid. All individual quantum numbers conform to their respective rules, such as the principal quantum number being an integer, the azimuthal quantum number being less than n.
Step-by-step explanation:
The set of quantum numbers provided in the question is 1, 0, 0, 1/2. To determine if this set is valid or not, we must check it against the rules of quantum mechanics. The first quantum number (n) is the principal quantum number, which indicates the energy level and is an integer starting from 1. Here, n is 1, which is valid.
The second quantum number (l) is the azimuthal quantum number, which indicates the subshell and must be in the range of 0 to (n-1). Since n is 1 and l is 0, this is also valid because it obeys the rule that l must be less than n.
The third quantum number (ml) is the magnetic quantum number and it represents the orbital orientation in space. It should be in the range from -l to +l, including zero. Since l is 0 in this case, ml must also be 0, which it is, so this is valid.
Finally, the fourth quantum number (ms) is the spin quantum number, which can be either +1/2 or -1/2. In this set, ms is +1/2 which is a permitted value. Thus, the spin quantum number is also valid.
Since all individual quantum numbers follow the respective rules, the overall set {1, 0, 0, 1/2} of quantum numbers is indeed allowed for an electron in an atom.
To provide further context, in a hydrogen atom, there can be two sets of quantum numbers for the single electron it possesses. According to the Pauli exclusion principle, if there were two electrons, they would have the quantum numbers {1, 0, 0, +1/2} and {1, 0, 0, -1/2} respectively, because they can occupy the same orbital only if their spins are opposite.