PLEASE BE CLEAR AND COMPLETE NO PHOTO\'S PLEASE Explain why each of the followin

Question

PLEASE BE CLEAR AND COMPLETE NO PHOTO'S PLEASE

Explain why each of the following sets of quantum numbers (n, l, ml, ms) is not permitted for hydrogen.

(a) (2,1,+1,1/2)

1) l exceeds the maximum permitted value.

2) ml exceeds the maximum permitted value.    

3) ms can be only +1/2 or 1/2.

4) l cannot be negative.

5) such state is permitted.

(b)   (4,1,+1,+5/2)

1) l exceeds the maximum permitted value.

2) ml exceeds the maximum permitted value.    

3) ms can be only +1/2 or 1/2.

4) l cannot be negative.

5) such state is permitted.

(c) (3,1,+3,+1/2)

1) l exceeds the maximum permitted value.

2) ml exceeds the maximum permitted value.    

3) ms can be only +1/2 or 1/2.

4) l cannot be negative.

5) such state is permitted.

(d) (2,3,1,1/2)

1) l exceeds the maximum permitted value.

2) ml exceeds the maximum permitted value.    

3) ms can be only +1/2 or 1/2.

4) l cannot be negative.

5) such state is permitted.

Explanation / Answer

For a given n, l can range from 0 to n-1, ml can range from -l to +l and ms can be +-1/2 only
applying the above rules

a. l is given to be -1, but l cannot be negative, so 4
b. ms is given 5/2, but ms can be only +1/2 or 1/2, so 3
c. ml can range from -l to +l, and given l is 1, so ml has to be 1,0 or -1, but ml is given 3, so ml exceeds the maximum permitted value -> 2
d. l can have values from 0 to n-1, given n = 2, so l can be 0,1,2, but given l = 3, so l exceeds the maximum permitted value -> 1

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