Final answer:
The 4f sublevel has 7 possible m values. The m values, or magnetic quantum numbers, for any f sublevel range from -3 to +3, which includes -3, -2, -1, 0, 1, 2, and 3. Therefore, there are 7 m values for the 4f sublevel.
Step-by-step explanation:
The 4f sublevel can hold a maximum of 14 electrons. According to the Aufbau principle, electrons fill the sublevels in order of increasing energy. For the 4f sublevel, there are 7 orbitals, each with a different magnetic quantum number (m).
The values of m for the 4f sublevel range from -3 to +3. Therefore, there are a total of 7 different m values for the 4f sublevel.