Question

Give all possible ml values for orbitals that have each of the following: (a) l = 3; (b) n = 2; (c) n = 6, l = 1.

Answer 1

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

(a) At l = 3,  $m_l=+3,+2,+1,0,-1,-2,-3$

(b) l = 0, 1

At l = 0,  $m_l=0$

At l = 1,  $m_l=+1,0,-1$

(c) At l = 1,  $m_l=+1,0,-1$

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) l = 3 then the value of 'ml' is,

At l = 3,  $m_l=+3,+2,+1,0,-1,-2,-3$

(b) n = 2 then the value of 'ml' is,

l = 0, 1

At l = 0,  $m_l=0$

At l = 1,  $m_l=+1,0,-1$

(c) n = 6 and l = 1 then the value of 'ml' is,

n = 6

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

At l = 1,  $m_l=+1,0,-1$