Question

Are the following quantum number combinations allowed? If not, show two ways to correct them:
(a) n = 1; l = 0; ml = 0
(b) n = 2, l = 2; ml = +1
(c) n = 7, l = 1; ml = +2
(d) n = 3, l = 1; ml = -2

Answer 1

Answer : All possible values of 'ml' for the following orbitals are:

(a) This combinations is allowed.

(b) This combinations is not allowed.

(c) This combinations is not allowed.

(d) This combinations is not allowed.

Explanation :

There are 4 quantum numbers :

Principle Quantum Numbers : It describes the size of the orbital. It is represented by n. n = 1,2,3,4....

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 m_l. The value of this quantum number ranges from $(-l\text{ to }+l)$. When l = 2, the value of $m_l$ will be -2, -1, 0, +1, +2.

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

(a) n = 1; l = 0; ml = 0

n = 1

l = 0

At l = 0,  $m_l=0$

This combinations is allowed.

(b) n = 2, l = 2; ml = +1

n = 2

l = 0, 1

At l = 0,  $m_l=0$

At l = 1,  $m_l=+1,0,-1$

This combinations is not allowed because l = 2 is not feasible for n = 2.

(c) n = 7, l = 1; ml = +2

n = 7

l = 0, 1, 2, 3, 4, 5, 6

At l = 0,  $m_l=0$

At l = 1,  $m_l=+1,0,-1$

At l = 2,  $m_l=+2,+1,0,-1,-2$

At l = 3,  $m_l=+3,+2,+1,0,-1,-2,-3$

At l = 4,  $m_l=+4,+3,+2,+1,0,-1,-2,-3,-4$

At l = 5,  $m_l=+5,+4,+3,+2,+1,0,-1,-2,-3,-4,-5$

At l = 6,  $m_l=+6,+5,+4,+3,+2,+1,0,-1,-2,-3,-4,-5,-6$

This combinations is not allowed because ml = +2 is not feasible for l = 1.

(d) n = 3, l = 1; ml = -2

n = 3

l = 0, 1, 2

At l = 0,  $m_l=0$

At l = 1,  $m_l=+1,0,-1$

At l = 2,  $m_l=+2,+1,0,-1,-2$

This combinations is not allowed because ml = -2 is not feasible for l = 1.