Question

a. An atomic orbital has `n=3`. What are the possible values of `l` and `m`?
b. List the quantum numbers `(m and l)` of electrons for `3d` orbital.
c. Which of the following orbitals are possible" `1p, 2s, 2p,` and `3f`?

Answer 1

n=3 ( Given)
for a given value of n , l can have values from 0 to (n-1)
for n= 3
l=0,
for a given value of l, `m_(l) ` can have (2l +1) values.
for n = 3
l=0,1,2
for l=0, m=0
l=1 , m=-1 , 0 , 1
l=2 , m =-2, -1, 0,1,2
for n =3
`m_(0) =0`
`m_(1) =-1,0,1`
`m_(2) = 2,-1,0,1,2`
(ii) for 3d orbial l=2
for a given value orbitals only 2s and 2p are possible 1p and 3f cannot exist .
for p- orbital l=1
for a given value of n ,l can have values form zero to (n-1)
for is equal to 1, the minmum value of n is 2 .
similarly
for f - orbital l=4
for l=4 the minmum value of n is 5 .
hence, 1p and 3f do not exist .