Final answer:
For an electron in the 3s orbital, the possible sets of quantum numbers are (3, 0, 0, +1/2) and (3, 0, 0, -1/2), reflecting its energy level, orbital shape, orientation, and two possible spin states.
Step-by-step explanation:
An electron in the 3s orbital has a specific set of four quantum numbers that describe its state. These are the principal quantum number (n), the angular momentum quantum number (l), the magnetic quantum number (ml), and the spin quantum number (ms). For an electron in the 3s orbital, the principal quantum number n is always 3. This reflects the energy level of the electron and indirectly, its distance from the nucleus.
The angular momentum quantum number l defines the shape of the orbital and for an s-orbital, this value is always 0, since s-orbitals are spherical. The magnetic quantum number ml describes the orientation of the orbital and for an s-orbital, which does not depend on orientation, this number is also 0.
Finally, the spin quantum number ms, which can be either +1/2 or -1/2, indicates the two possible spin states of an electron. Therefore, the only difference in the quantum numbers for two electrons in a 3s orbital is in their spin quantum numbers.
Conclusively, the all possible sets of quantum numbers for an electron in the 3s orbital are (n=3, l=0, ml=0, ms=+1/2) and (n=3, l=0, ml=0, ms=-1/2).