Sapling homework

[Natallie K 3B]

How many electrons in an atom could have these sets of quantum numbers?
n=3

n=4,l=2

n=7,l=3,ml=−1

I am confused as how to solve this problem?

[Lucy Wang 2J]

The question is basically asking how many electrons could have these criteria.

so for the first one, n=3

The 3 shell has 3s, 3p, 3d and in each of these subshells they can contain 2, 6, 10 electrons respectively. Then add them together and the answer is 18.

For the second question, n=4, l=2
This is referring to the 4d subshell which can only contain 10 electrons

finally for n=7, l=3, ml=-1
This is referring to the ml=-1 orbital within the 7f subshell. Since an orbital can hold a max of 2 electrons, the answer is 2.

[VincentLe_3A]

To solve these problems, you look at the specificity of the quantum numbers given. For example, in the first problem you are given n=3, so you know it is talking about the 3rd energy shell. In the third shell, you have s, p, and d orbitals (you can figure this out by finding the allowed values of l, which are l= 0,1,2,..n-1). Since none of the orbitals are specified, there are 2 possible electrons in s, 6 in p, and 10 in d, so there are 18 electrons in total that can share this principle quantum number. The second and third problems get more specific. For example, the second problem is asking about possible electrons in only the 4d orbital. The third question gets even more specific mentioning the orbital of the 7f subshell, which only two electrons can be oriented in. Overall, it is just a matter of going through the quantum numbers given and sort of translating the numbers into energy level, subshell, orbitals of subshells, and spin of the orbitals of subshells as much as possible.

Hope this helps.