Question

How many electrons in an atom could have these sets of quantum numbers?

(a) n=3

(b) n=4, l=2

(c) n=7, l=3, ml=-1

 

Answer 1

(a) for n=3 total number of electron will be 18

as total number of electron with principal quantum number(n) T=2*n*n, so for n=3 t=2*3*3=18.

description

for n=3 we can have following set of quantum number

n=3 ,l=0,1,2.

for l=0 we can have m=0 and s=1/2 and s=-1/2 total(T1)=2*1=1

for l=1 we have m=-1,0,-1 and for each m we have s=-1/2 and 1/2 so total will be(T2)=2*3=6

simailarly for n=2 we have l=-2,-1,0,1,2 and for ecah m there are two s values so tota(T3)=2*5=10

adding all 3 total above we get t=18.

(b)n=4 l=2

for this we have the following set of quantum niumbers

n=4 l=2,m=-2,-1,0,1,2

for each m value we have 2 svalue so total no electron is T=2*n(m)=2*5=10,where n(m) is number of m values(magnetic quantum numbers)

(c)n=7,l=3,m=-1

here only one m(magnetic quantum jumber) value is given so only two electrons having s=1/2 and s=-1/2 arepossible