Question

(a) How many ℓ values are associated with n = 1? (b) How many mℓ are associated with ℓ= 4?

Answer 1

Here we know that

n = principal quantum number

l = Orbital angular momentum quantum number

m_l = magnetic quantum number,

Now Value of each quantum number can be

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

then l = 0 to (n - 1)

then m_l = -l to +l,

Part A.

l values which are associated with n = 1, will be:

when n = 1, then

l = 0 to (n - 1) = 0 to 0

So for n = 1, l = 0

And only one value is associated with n = 1

(1 values)

Part B.

when l = 4, then

ml = -l to +l, So

ml = -4 to +4, So

ml = -4, -3, -2, -1, 0, 1, 2, 3, 4

So there are 9 different ml values are associated with l = 4.

(9 Values)

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