Question

State which of the following set of quantum number would be possible and which would be permissible for an electron in an atom.

a) n=3, l=3, m l =+3 , m s = +1/2
b) n=3, l=0, m l =+1 , m s = - 1/2
c) n=5, l=4, m l =+3 , m s = 1
d) n=0 ,l=0, m l = 0 , m s = +1/2
e) n=4, l=3, m l = - 2 , m s = - 1/2

Answer 1

The correct option is: e) n=4, l=3,
`m_(l)` = - 2 ,
`m_(s)` = - 1/2

Step-by-step explanation:

The four quantum numbers that describe the electrons in an atom are: The principal: n, azimuthal: l, magnetic: m, and spin: s.

For a given electron, the values of the quantum numbers should be in the given range- principal quantum number: n ≥ 1;

azimuthal quantum number: 0 ≤ l ≤ n − 1;

magnetic quantum number: −l ≤
`m_(l)` ≤ +l;

spin quantum number: −s ≤
`m_(s)` ≤ +s

Now, for n= 4,

The value of l: 0 to n − 1 = 0 to 3 = 0, 1, 2, 3

The value of
`m_(l)` for l= 3 : -3 to +3 = -3, -2, -1, 0, +1, +2, +3

The value of
`m_(s)`: -1/2, +1/2

Therefore, the given set of quantum numbers: n=4, l=3,
`m_(l)` = - 2 ,
`m_(s)` = - 1/2; are possible and permissible for an electron in an atom.