Question

1. what are the possible ( m_{l} ) values for the following types of orbitals?

a. ( s )
b. ( p )
c. ( d )
d. ( f )

Explanation:

• For an \(s\) orbital, the angular momentum quantum number \(l = 0\). The magnetic quantum number \(m_{l}\) ranges from \(-l\) to \(+l\) in integer steps. So when \(l = 0\), \(m_{l}=0\).
• For a \(p\) orbital, \(l = 1\). Then \(m_{l}\) values are \(- 1,0,+1\) (since \(m_{l}=-l,-l + 1,\cdots,l-1,l\)).
• For a \(d\) orbital, \(l = 2\). So \(m_{l}=-2,-1,0,+1,+2\).
• For an \(f\) orbital, \(l = 3\). Thus \(m_{l}=-3,-2,-1,0,+1,+2,+3\).

Answer:

a. \(m_{l}=0\)
b. \(m_{l}=-1,0,+1\)
c. \(m_{l}=-2,-1,0,+1,+2\)
d. \(m_{l}=-3,-2,-1,0,+1,+2,+3\)