Show the permissible values of l and m

[Tyyoung]

Homework Statement

Show the permissible values of l and m for;
a) n=1
b) n=2
c) n=3

Homework Equations

I'm not really sure what they mean by permissible values, I would greatly appreciate it if someone could explain this to me and help me get started. thank you

The Attempt at a Solution

 

[mgb_phys]

I think you need to give us a little more information

 

[Tyyoung]

n is the primary quantum number, l is the secondary quantum nuber and m is the magnetic quantum number.

if n=1 then you have 1 sublevel you use the equation n^2 to find out how many orbitals it has. For example, if n=2 then sub it into the equation n^2 so (2)^2 = 4, therefore it has 4 orbitals. Umm lol This information is only semi relevant I believe I'm not really understanding the question itself so it makes it difficult to relate information to it. There isn't a direct formula that I know of that is related to it I think it is a question that you have to infer but once again I don't exactly understand what the question is asking.

 

[Borek]

It asks what values can l & m take for a given n.

Let's say... if n=4, is it possible to have l=7?

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methods

 

[DeeNos]

The permissible values of l and m depend on the quantum numbers n, l, and m. The quantum number n represents the principal energy level, l represents the angular momentum quantum number, and m represents the magnetic quantum number. The permissible values of l and m can be determined using the following guidelines:

a) For n=1, the only permissible value of l is 0, and the only permissible value of m is 0.

b) For n=2, the permissible values of l are 0 and 1, and the permissible values of m are -1, 0, and 1.

c) For n=3, the permissible values of l are 0, 1, and 2, and the permissible values of m are -2, -1, 0, 1, and 2.

These values can be determined by considering the possible combinations of n, l, and m that satisfy the equation l = 0, 1, 2,..., n-1 and m = -l, -l+1, -l+2,..., l-1, l. It is important to note that the values of l and m must satisfy the condition that l < n and -l ≤ m ≤ l. These permissible values of l and m are important in understanding the energy levels and electron configurations of atoms.