Final answer:
For an l = 2 electron, the angular momentum vector L can make five different angles with the z-axis, which correspond to the five possible values of the magnetic quantum number ml.
Step-by-step explanation:
The number of angles that the angular momentum vector L can make with the z-axis for an electron with quantum number l = 2 is determined by the magnetic quantum number ml, which can take on the values -l to +l in integer steps.
Since l = 2, ml can have five different values: -2, -1, 0, 1, and 2, which corresponds to five different angles. The smallest angle corresponds to the maximum value of the magnetic quantum number, which would be ml = 2 in this case.