Final answer:
The total number of orbitals at a given main energy level, n, is given by the formula 2n². Thus, the correct option is b. 2n², resulting in 2 orbitals for n=1 and 8 orbitals for n=2, where each orbital can hold two electrons.
Step-by-step explanation:
The total number of orbitals that can exist at a given main energy level, n, is determined by the formula 2n². Therefore, the correct answer to the question is option b. 2n².
For example, at the first energy level (n=1), applying the formula results in 2(1)² = 2 orbitals. Similarly, for the second energy level (n=2), it results in 2(2)² = 8 orbitals.
It is important to note that each orbital can hold a maximum of two electrons.The principal quantum number n specifies the shell and, hence, the general range for the energy of the orbitals within a shell. These shells and the orbitals within them are key in understanding electron configurations and the structure of atoms.