Quantum numbers arise naturally from the mathematics used to describe the possible states of an electron in an atom.
The four quantum numbers, the principal quantum number (n), the angular momentum quantum number (l), the magnetic quantum number (ml), and the spin quantum number (ms) have strict rules which govern the possible values.
Identity allowable combinations of quantum numbers for an electron. Select all that apply.

a) n = 3, l = 2, ml = −2, ms = −1/2
b) n = 4, l = 0, ml = 1, ms = −1/2
c) n = 3, l = −2, ml = −2, ms = +1/2
d) n = 5, l = 4, ml = 4, ms = +1/2
e) n = 3, l = 3, ml = 1, ms = +1/2
f) n = 2, l = 1, ml = 0 ,ms = 0

Azimuthal Quantum Number : It describes the shape of the orbital. It is represented as 'l'. The value of l ranges from 0 to (n-1). For l = 0,1,2,3... the orbitals are s, p, d, f...

Magnetic Quantum Number : It describes the orientation of the orbitals. It is represented as . The value of this quantum number ranges from . When l = 2, the value of will be -2, -1, 0, +1, +2.

Spin Quantum number : It describes the direction of electron spin. This is represented as The value of this is [tex]+\frac{1}{2}[/tex] for upward spin and [tex]-\frac{1}{2}[/tex] for downward spin.

a) n= 3, l = 2, [tex]m_l=-2[/tex] , [tex]m_s=-\frac{1}{2}[/tex]

n=3 and l can have value 0 to (n-1) i.e. 0, 1 and 2.

[tex]m_l[/tex] can have values from -l to +l i.e for l= 2 , [tex]m_l[/tex] can have values -2, -1, 0 , +1 and +2. Thus is allowed.

b) n= 4, l= 0, [tex]m_l=-1[/tex] , [tex]m_s=-\frac{1}{2}[/tex]

n= 4 and l can have value 0 to (n-1) i.e. 0, 1 , 2 and 3.

[tex]m_l[/tex] can have values from -l to +l. For l= 0 , [tex]m_l[/tex] can have value of 0 only. Thus is not allowed.

c) n= 3 , l= -2, [tex]m_l=-2[/tex] , [tex]m_s=+\frac{1}{2}[/tex]

n= 3 and l can have value 0 to (n-1) i.e. 0, 1 and 2. Thus is not allowed.

d) n= 5, l= 4, [tex]m_l=4[/tex] , [tex]m_s=+\frac{1}{2}[/tex]

n= 5 and l can have value 0 to (n-1) i.e. 0, 1 , 2 ,3 and 4

[tex]m_l[/tex] can have values from -l to +l. For l= 4 , [tex]m_l[/tex] can have value of -4, -3, -2 , -1, 0 , +1, +2, +3 and +4. Thus is allowed.

e) n= 3, l= 3, [tex]m_l=1[/tex] , [tex]m_s=+\frac{1}{2}[/tex]

n= 3 and l can have value 0 to (n-1) i.e. 0, 1 and 2.

[tex]m_l[/tex] can have values from -l to +l. For l= 3 , [tex]m_l[/tex] can have value of -3, -2 , -1, 0 , +1, +2, and +3. Thus is allowed.