Final answer:
All the subshells mentioned, including 4f, 4s, 4p, and 4d exist. They are allowed subshells within the constraints of the angular momentum quantum number, where the azimuthal quantum number ranges from 0 to n-1.
Step-by-step explanation:
The question asks which of the subshells below do not exist due to the constraints upon the angular momentum quantum number. Each subshell is represented by a principal quantum number (n) and an azimuthal quantum number (l), where l is in the range from 0 to n-1. Subshells are usually designated as s (l=0), p (l=1), d (l=2), and f (l=3). Based on these rules:
- 4f is allowed (n=4, l=3)
- 4s is allowed (n=4, l=0)
- 4p is allowed (n=4, l=1)
- 4d is allowed (n=4, l=2)
All of the above subshells exist. Consequently, the correct answer is e. All of the above exist.
Using the formula 2n², we can calculate the number of electrons in a given shell, and 2(2l + 1) to find the maximum number of electrons in a specific subshell. For example, the fourth shell (n=4) can hold up to 2n² = 2(4)² = 32 electrons, and within the 4d subshell (l=2), it can hold up to 2(2l + 1) = 2(2(2) + 1) = 10 electrons.