Question

State which of the following set of quantum number would be possible and which would be permissible for an electron in an atom. a) n=3, l=3, m l =+3 , m s = +1/2 b) n=3, l=0, m l =+1 , m s = - 1/2 c) n=5, l=4, m l =+3 , m s = 1 d) n=0 ,l=0, m l = 0 , m s = +1/2 e) n=4, l=3, m l = - 2 , m s = - 1/2

Answer 1

hey...
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Basically,
   Principal quantum number = n
   Azimuthal quantum number = l = 0 to (n-1)
   Magnetic quantum number = m = -l to +1
   Spin quantum number = s = +1/2 or -1/2
Now,
   (i)   n=3; l=2; m=2; s=+1/2
          n=3
          l = 0 to (n-1) = 0 to 2 = here it is 2 which is permissible
          m = -l to +l = -2 to +2 = here it is 2 which is permissible
          s = +1/2 or -1/2 = here it is +1/2  whch is permissible

   (ii)  n=3; l=4; m=0; s=-1/2
          n=3
          l = 0 to (n-1) = 0 to 2 = here it is 4 which is not permissible
         
   (iii) n=4; l=0;m=2; s=+1/2
          n=4
          l = 0 to (n-1) = 0 to 2 = here it is 0 which is permissible
          m = -l to +l = 0 = here it is 2 which is not permissible and moreover m should always be less than l.
 
   (iv) n=4; l=4; m=3; s=+1/2
          n=4
          l = 0 to (n-1) = 0 to 3 = here it is 4 which is not permissible.

Answer 2

Answer is 4

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