Final answer:
The number of electrons that can be assigned to orbitals designated by quantum numbers n = 7, ℓ = 1 is 12. In a ground state atom of As, there are a total of 20 electrons with the quantum number ℓ = 2.
Step-by-step explanation:
In quantum mechanics, the number of electrons that can be assigned to an orbital is determined by the quantum numbers. The first quantum number, n, represents the shell and it can have values of 1, 2, 3, and so on. The second quantum number, ℓ, represents the subshell and it can have values from 0 to n-1. So, for the quantum numbers n = 7 and ℓ = 1, we are in the 7p subshell. In the 7p subshell, there are a total of 6 orbitals, each capable of holding 2 electrons. Therefore, the number of electrons that can be assigned to orbitals designated by n = 7 and ℓ = 1 is 12.
In a ground state atom of As (arsenic), the quantum number ℓ = 2 corresponds to the d subshell. In the d subshell, there are a total of 10 orbitals, each capable of holding 2 electrons. Therefore, the number of electrons with the quantum number ℓ = 2 in a ground state atom of As is 20.