Hi. Can someone please answer this CORRECTLY and clarify question #1. Why 4 sets

Question

Hi. Can someone please answer this CORRECTLY and clarify question #1.
Why 4 sets of numbers? I thought there would be 6 sets as follows:
1. (3, 1, -1, -1/2) 2. (3, 1, 0, -1/2) 3. (3, 1, +1, -1/2) 4. (3, 1, -1, +1/2) 5. (3, 1, 0, +1/2) 6. (3, 1, +1, +1/2) 1. Sulfur has FOUR electrons in the 3p subshell. Describe each of these four electrons with an appropriate set of four quantum numbers using the notation (n, 1, mi, ms Note that your answer should contain FOUR SETs with each set containing four quantum numbers. 2. Yttrium has the electron configuration [Kr] 5s24d1. Describe each of the three valence electrons of yttrium with an appropriate set of four quantum numbers using the notation (n, 1, mi, ms).

Explanation / Answer

As question, electronic configuration of sulphur =[Ne] 3s² 3p

So, there are six electrons in valence shell but the question is asking for four electrons in 3p subshell.so, Do not confuse with it,

The first quantum number tells you which energy level electron, which is same for all four electron i.e. n=3

The second number tells you which sublevel the electron is in - all four are in the 3p sublevel, so l=1. We use s=0, p=1, d=2, f=3

The third quantum number tells you which orbital of the sublevel an electron is in. The three orbitals of the 3p sublevel will each filled with an up spin electron first, so ms=1/2 and left most orbital will get also down spin, so m s =-1/2 electron The three orbitals for a p sublevel are labelled -1, 0, +1.Each three orbital get different its value. The first electron goes to the first orbital, then the second electron to second, the third electron to third and after that fourth electron fills the first orbital with down spin.

The final number tells you the spins, the four electrons with ml value as 1/2,1/2,1/2 and -1/2.

so finale value for these four electrons as below:-

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

(3,1,0,1/2)

(3,1,1,1/2)

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

2. electronic configuration of yttrium =[Kr] 5s2 4d1

There are 3 electrons in valence shell,

The first quantum number tells you which energy level electron, which is same for all four electrons i.e. n=5 for two electrons, n=4 for the third electron.

The second number tells you which sublevel the electron is in - all four are in the 3p sublevel, so l=0 for two electrons and l=2 for the third electron.

The third quantum number tells you which orbital of the sublevel an electron is in. The orbital of the 5s sublevel will each filled with an up spin electron first, ms =1/2 and filled with down spin so ms =-1/2.The five orbitals of a d sublevel are labelled -2,-1, 0, +1,+2. so, the only first orbital is filled so, it's ml value = -2 and one orbital of s subshell is filled with two electrons, it's ml value = 0.

The finale quantum value for three electrons are as below:-

( 5,0,0,+1/2)

( 5,0,0,-1/2)

( 4,2,-2,+1/2)

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