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Spin Quantum Number Table of Contents

1. 1. Spin Quantum Number 

2. 2. Combinations of Quantum Numbers

3. 3. Questions

4. 4. Answers

5. 5. References

The Spin Quantum Number (s is a !a"ue (of 1#2 that $escribes the an%u"ar momentum of an e"ectron. An e"ectron

spins aroun$ an a&is an$ has both an%u"ar momentum an$ orbita" an%u"ar momentum. 'ecause an%u"ar momentum

is a !ector the Spin Quantum Number (s has both a ma%nitu$e (1#2 an$ $irection () or *. This !ector is ca""e$ the

ma%netic spin +uantum number (ms.

Spin Quantum Number ,ach orbita" can on"- ho"$ two e"ectrons. ne e"ectron wi"" ha!e a )1#2 spin an$ the other wi"" ha!e a *1#2 spin.

,"ectrons "i/e to fi"" orbita"s before the- start to pair up. Therefore the first e"ectron in an orbita" wi"" ha!e a spin of 

)1#2. After a"" the orbita"s are ha"f fi""e$ the e"ectrons start to pair up. This secon$ e"ectron in the orbita" wi"" ha!e a

spin of *1#2. 0f there are two e"ectrons in the same orbita" it wi"" spin in opposite $irections as shown in the fi%ure

be"ow

http##www.broo/"-n.cun-.e$u#bc#ahp#...3+uant4.%if 

Combinations of Quantum Numbers• The three +uantum numbers (n l  an$ m that $escribe an orbita" are inte%ers 1 2 3.

• The principa" +uantum number (n cannot be ero. The a""owe$ !a"ues of n are therefore 1 2 3 4...

• The an%u"ar +uantum number (l  can be an- inte%er between an$ n * 1.

o 0f n  3 l  can be either 1 or 2.

• The ma%netic +uantum number (m can be an- inte%er between *l  an$ )l .

o 0f l   2 m can be *2 *1 )1 or )2.

• rbita"s that ha!e same !a"ue of principa" +uantum number form a She""(n.

• rbita"s within the she""s are $i!i$e$ into subshe"" ("

o sl    pl   1 d l   2 f l   3

Questions

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1. 6hat is the spin +uantum number for Tun%sten (s-mbo" 67

2. 6hat is the spin +uantum number for 8o"$ (s-mbo" Au7

3. 6hat is the spin +uantum number for Su"fur (s-mbo" S7

Answers1. 6hat is the spin +uantum number for Tun%sten (s-mbo" 67

Tun%sten has 4 e"ectrons in the 5$ orbita". Therefore 1 e"ectron wi"" %o into each orbita" (no pairin%. The 4th e"ectron

wi"" ha!e a )1#2 spin.

2. 6hat is the spin +uantum number for 8o"$ (s-mbo" Au7

8o"$ has 9 e"ectrons in the 5$ orbita". Therefore the e"ectrons wi"" start to pair up which means the 9th e"ectron wi""

pair up %i!in% it a *1#2 spin.

3. 6hat is the spin +uantum number for Su"fur (s-mbo" S7

Su"fur has 4 e"ectrons in the 3$ orbita"s. The 4th e"ectron in this orbita" wi"" be the first one to pair up with another

e"ectron therefore %i!in% it a *1#2 spin.

References1. :ousecroft Catherine ,. an$ A"an 8. Sharpe. Inorganic Chemistry . 3r$ e$. :ar"ow ;earson ,$ucation

2<. ;rint. (p% 15.

2. Nostran$ =an. ,nc-c"ope$ia of Chemistr-. 5th e$. >ohn 6i"e- an$ Sons 0nc. 25. ;rint. (p% 139?.

• ;re!ious 

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