Final answer:
In the main level n=1, the magnetic quantum number (m) can only have one value, which is 0. This is because the angular momentum quantum number (l) for this level is 0, restricting the range of m to just 0.
Step-by-step explanation:
The quantum magnetic numbers (m) in the main level (n=1) can be understood by considering the quantum mechanical model of the atom. When dealing with the quantum numbers for the main energy level (n=1), we first must recognize that the angular momentum quantum number (l) can only be 0 for this level. Consequently, as the magnetic quantum number (m) depends on the value of l, it too can only be 0, since it ranges from -l to +l, including zero. Therefore, for n=1, there is only one value for m, that is m=0. Additionally, there can be two electrons in the n=1 state, which would have the quantum numbers (1, 0, 0, +1/2) and (1, 0, 0, -1/2), accounting for their spin projections. Therefore, the correct answer to the question regarding the magnetic quantum numbers in the main level (n=1) is option c) 1.