Final answer:
The magnetic quantum number ml can range from -l to +l in integer steps, resulting in 2l + 1 possible values. For l = 0, ml is 0; for l = 1, ml ranges from -1 to +1; for l = 2, ml ranges from -2 to +2; and for l = 3, ml ranges from -3 to +3.
Step-by-step explanation:
The possible values of the magnetic quantum number ml depend on the value of the azimuthal quantum number l. For each value of l, ml can range from -l to +l in integer steps, meaning it can take 2l + 1 possible values.
- For l = 0, ml can only be 0.
- For l = 1, ml can be -1, 0, or +1.
- For l = 2, ml can be -2, -1, 0, +1, or +2.
- For l = 3, ml can be -3, -2, -1, 0, +1, +2, or +3.
Therefore, to answer the question:
- a. ml values for l = 0: {0}
- b. ml values for l = 1: {-1, 0, +1}
- c. ml values for l = 2: {-2, -1, 0, +1, +2}
- d. ml values for l = 3: {-3, -2, -1, 0, +1, +2, +3}