Every electron in an atom is described by a unique set of four quantum numbers:

Question

Every electron in an atom is described by a unique set of four quantum numbers: n, l, m_l, and m_s. The principal quantum number, n, identifies the shell in which the electron is found. The angular momentum quantum number, l, indicates the kind of subshell. The magnetic quantum number, m_l, distinguishes the orbital within a subshell. The spin quantum number, m_s species the electron spin. Identify which sets of quantum numbers are valid for an electron. Each set is ordered (n, l, m_l, m_s). 2, 1, -1, 1/2 3, -2, -2, -1/2 3, -2, -1, 0 1, 0, 0, -1/2

Explanation / Answer

we know n   = 1 to n

   l   = 0 to n-1

m = -l to +l

s   = ± 1

so 1) 2,1,-1,1/2

Here n = 2 so l = 0,1 m = 0,-1,0,+1   , s = ±1/2

      so 2,1,-1,1/2   is correct it is 2pz^1

2)     3,-2,-2,-1/2

Here n = 3 , so l =0,1,2 ,

Here l = -2 so this configuration is invalid

3) 3,-1,-1,0

As here n = 3 , l = 0,1,2   , s = ±1/2

Here l = -1 . s = 0 are wrong so this config is invalid

4) 1,0,0,-1/2

Here n = 1 , so l = 0 m = + 0 ,, s =±1/2

so this config is valid it is 2s^1 config

5)   4,3,5,-1/2

Here n = 4 so l = 0,1,2,3

                 when l = 0 , m =0 ,

when l = 1,m = -1,0,+1

when l = 2 , m = -2,-1,0,+1,+2

when l = 3, m = -3,-2,-1,0,+1,+2,+3

   s = ±1/2

So here n = 4 is correct , l = 3 is correct , m=5 is wrong , s = -1/2 is correct

as a whole configuration is invalid

6)   4,3,3, -1/2

Here n = 4 so l = 0,1,2,3

                 when l = 0 , m =0 ,

when l = 1,m = -1,0,+1

when l = 2 , m = -2,-1,0,+1,+2

when l = 3, m = -3,-2,-1,0,+1,+2,+3

   s = ±1/2

So this config is correct  

7) 0,1,1,-1/2

If n = 0, l =0, m= 0 , s = ±1/2

Here l=1 ,m=1 is not possible

so this config is invalid

8) 3,3,-1,1/2

here n= 3 , so l =0,1,2

so here l = 3 is not possible

so this config is invalid

9) 2,2,1,1/2

Here n = 2 so l = 0,1 m = 0,-1,0,+1   , s = ±1/2

So l = 2 is not possible

so this config is invalid

10) 1,1,0,1/2

Here n = 1 , l = 0, m = 0 , s =±1/2

so here l =1 , m=1 are wrong

so this config is invalid

11) 3,2,1,1/2

Here n = 3 , sol = 0,1,2

If l = 0, m=0

if l = 1 , m =-1,0,+1

if l =2,m = -2,-1,0,+1,+2

s = ± 1/2

so this config is possible

12) 2,1,-1,-1/2

Here n = 2 so l = 0,1 m = 0,-1,0,+1   , s = ±1/2

so this config is possible and valid

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