Answer:
(1). l= 0, 1, 2; the total number of orbitals possible at the n = 3 energy level is 9.
(2). m(l) = -1, 0, +1; the total number of orbitals possible at the l = 1 sublevel is 4.
Explanation:
Quantum numbers can simply be defined as the parameter which is used to define and describe the energy levels and the position of orbitals in a molecule. There are four basic types of quantum and they are;
1. The principal Quantum number(n): which has the values from 1, 2, 3,..., n. This number is used in describing the energy level of electron.
2.The magnetic quantum number: this is designated as m(l) and has the values of -l, ..., 0, ... , l.
3. The orbital angular momentum quantum number or azimuthal quantum number (l) : has the values of 0, 1, 2,..., (n-1) and this quantum number is use to determine electrons orbital or subshell.
4. The electron spin quantum number: it is designated with the symbol m(s) and it has values of either -½ or +½. It is used to show the direction of the spinning of electron.
==> Therefore if the value of n = 3, 3,The quantum number l can have values from 0, 1, 2. And this is because l= (n-1).
The total number of orbitals possible at the n = 3 energy level is 9. We used the formula n^2 to calculate the total number of orbitals possible at the n at any value that is for n = 3; 3^2 = 3×3 = 9.
===> For the value of l = 1, the quantum number m(l) can have values from -1, 0, +1. Since m(l) can only have values ranging from -l, ..., 0, ..., l.
The total number of orbitals possible at the l = 1 sublevel is 4. Since, l= n - 1, that is n = 2. So, n^2 = 2^2 = 2 × 2 = 4.
