Question

1. If the value of n = 3,The quantum number l can have values from _________ to _________.The total number of orbitals possible at the n = 3 energy level is _________. 2. If the value of l = 1,The quantum number ml can have values from _________ to _________.The total number of orbitals possible at the l = 1 sublevel is _________.

Answer 1

1.) l = 0 to 2 ; Total number of orbitals possible at n=3 energy level is 9

2.) if l = 1, quantum number ml can have values from (-1 to 1)

Total number of orbitals possible at l = 1 sublevel is 3

Step-by-step explanation:

When n= 3, which is the principal quantum number, the angular quantum number 'l' can only take values ranging from( 0 to n-1) that is, when n=3, l can range from (0,1,2). Number of orbitals in a shell is the square of the principal quantum number,. Here 3^2 = 9. A total of 9 orbitals exist in the n=3 energy level with 1 in the 3s subshell, 3 in the 3p subshell and 5 in the 3d subshell.

The magnetic quantum number ranges from (-l to +l) therefore, with l being 1, ml can range from (-1 to 1) values -1, 0, 1. The number of orbitals in a subshell is 2(l) + 1

With l = 1;

2(l) + 1

2(1) + 1 = 3

Answer 2

(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.

Step-by-step 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.