For each of the following sublevels, give the n and l values and the number of orbitals.
(a) 3s
(b) 5f
(c) 5g
s electrons have "ell" = 0 and 3s has n = 3.
5f. n= 5. "ell" = 3
s,p,d,f have ell values of 0,1,2,3.
To determine the n and l values and the number of orbitals for each sublevel:
(a) 3s:
The sublevel "s" corresponds to the l value of 0. For the given sublevel, n is 3.
To find the number of orbitals, use the formula 2l + 1. Since l is 0 for the s sublevel, there is only one orbital in the 3s sublevel.
So, for 3s:
n = 3
l = 0
Number of orbitals = 1
(b) 5f:
The sublevel "f" corresponds to the l value of 3. For the given sublevel, n is 5.
Here, l=3 means that the "f" sublevel has 7 orbitals.
So, for 5f:
n = 5
l = 3
Number of orbitals = 7
(c) 5g:
The sublevel "g" is a hypothetical sublevel that is not currently used to describe atomic orbitals. In the current atomic model, the orbital shapes are described from s, p, d, and f sublevels. So, there is no l value or number of orbitals for the 5g sublevel.
To determine the n and l values for each sublevel, we can use the following rules:
- The n value represents the principal quantum number and is equal to the energy level of the electron.
- The l value represents the azimuthal quantum number and is equal to the type of sublevel within an energy level. It ranges from 0 to n-1, with 0 representing the s sublevel, 1 representing the p sublevel, 2 representing the d sublevel, and so on.
- The number of orbitals within a sublevel is given by 2l + 1.
Using these rules, we can determine the values for each sublevel:
(a) 3s:
- n = 3 (since it is in the third energy level)
- l = 0 (since it is an s sublevel)
- Number of orbitals = 2(0) + 1 = 1
(b) 5f:
- n = 5 (since it is in the fifth energy level)
- l = 3 (since it is an f sublevel)
- Number of orbitals = 2(3) + 1 = 7
(c) 5g:
- The g sublevel does not exist in the periodic table, as it is not within the allowed values of l (0 to n-1). Therefore, we cannot determine the n and l values or the number of orbitals for 5g.