Learning Goal: To understand and be able to use the rules for determining allowable orbital angular momentum states. Several numbers are necessary to describe the states available to an electron in the hydrogen atom. The principal quantum number nnn determines the energy of the electron. The orbital quantum number lll determines the total angular momentum of the electron, and the magnetic quantum number mlmlm_l determines the component of the angular momentum parallel to a specific axis, usually the z axis.

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Step-by-step explanation:

1) for a given n value the l value can be from 0 to n-1

So if n= 5 it can take 0,1,2,3,4 i.e it can take 5 values

2)for an electron with l =3

it can be from -3 -2 -1 0 1 2 3

i.e it can take 7 values

3) n = 3 !!

l = 0 , 1 , 2

for l=0 , m = 0 total = 0

for l= 1 ,m = -1,0,1 total = 3

for l = 2, m=-2,-1,0,1,2 total = 5

5+3+0 = 8

total possible states = 8x2=16

Answer is 16

4)given l=3 and n=3

orbital quantum number cannot be equal to principal quantum number

its max value is l-1 only

5)L = sqrt(l(l+1))x h'

for it to be max l should be max

for n = 3 max l value is 2

therefore it is sqrt(2(2+1)) x h'

sqrt(6) x h'

this is the answer