Question

If an electron is in the n=3 state l=1, list the possible quantum states (n, l, ml, ms).

(n, l, m,, m)

Answer 1

Here we know that

n = principal quantum number

l = Orbital angular momentum quantum number

ml = magnetic quantum number,

ms = spin quantum number

Now Value of each quantum number can be

n = 1, 2, 3, 4, 5 .......

then l = 0 to (n - 1)

then ml = -l to +l,

then ms = +1/2, -1/2

Now in this scenario given that n = 3 and l = 1, So

ml can have three different values: -1, 0, +1

ms, spin quantum number have two different value for each ml: -1/2, +1/2

So, possible quantum states (n, l, ml, ms) will be:

(3, 1, -1, -1/2), (3, 1, -1, +1/2), (3, 1, 0, -1/2), (3, 1, 0, +1/2), (3, 1, 1, -1/2), (3, 1, 1, +1/2)

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