In quantum mechanics, the principal quantum number (n) indicates the energy level of an electron in an atom. When n = 4, we can derive the possible values for the azimuthal quantum number (l), the magnetic quantum number (ml), and the spin quantum number (ms).
1. Possible values of l:
The azimuthal quantum number (l) can take on any integer value from 0 to (n-1). For n = 4, the possible values of l are:
- l = 0 (s orbital)
- l = 1 (p orbital)
- l = 2 (d orbital)
- l = 3 (f orbital)
2. Possible values of ml:
The magnetic quantum number (ml) can take on values ranging from -l to +l, including zero. Thus, for each value of l, we find the corresponding values of ml:
- For l = 0: ml = 0
- For l = 1: ml = -1, 0, +1
- For l = 2: ml = -2, -1, 0, +1, +2
- For l = 3: ml = -3, -2, -1, 0, +1, +2, +3
3. Possible values of ms:
The spin quantum number (ms) describes the intrinsic spin of an electron and can take one of two values:
- ms = +1/2
- ms = -1/2
In summary, for n = 4, the possible quantum numbers are:
- Values of l: 0, 1, 2, 3
- Values of ml: Based on l
- Values of ms: +1/2, -1/2