# What Is Z component of orbital angular momentum? How can we find the Z component? What is its importance? What does it resemble?

##### 1 Answer

You seem to be referring to *total orbital angular momentum*

Practically speaking, for general chemistry, you can simply use the value of

#bb(m_l = {-l,-l+1, . . . , 0, . . . , l - 1, l})#

For instance, if

#m_l = {-2,-1,0,+1,+2}#

That means five

**RELATION TO THE Z-COMPONENT OF THE TOTAL ORBITAL ANGULAR MOMENTUM**

Recall that the Schrodinger equation is typically written as

Well, it turns out that **wave function** describing the state of a quantum mechanical system, can be separated into a *radial* and an *angular* component,

#psi_(nlm_l)(r,theta,phi) = R_(nl)(r)Y_(l)^(m_l)(theta,phi)#

where

Traditionally, *eigenvalue* (the quantity we expect to see over and over again), in units of

This eigenvalue corresponds to the *operator* for **the** **component of the total orbital angular momentum**.

What we just said can be expressed as:

#stackrel("Operator")overbrace(hatL_z)" "stackrel("Angular")stackrel(" Component")stackrel("of Wave Function")overbrace(Y_(l)^(m_l)(theta,phi)) = stackrel("Eigenvalue")overbrace(m_lℏ)" "stackrel("Angular")stackrel(" Component")stackrel("of Wave Function")overbrace(Y_(l)^(m_l)(theta,phi))#

If **the phenomenon we can observe that corresponds to the magnetic quantum number**

**PHYSICS PERSPECTIVE**

Visually, in the presence of a magnetic field in the *total orbital angular momentum*) occurs along the

This is the event described by

For instance, when

And each

For instance:

- An
#m_l# of#1# corresponds to the upper half of the#2p_z# orbital. - An
#m_l# of#0# is the dot at the origin. - An
#m_l# of#-1# corresponds to the lower half.

**CHEMISTRY PERSPECTIVE**

From a practical point of view, what we really care about is how to use

- The number of
#m_l# values tells you the number of orbitals in a subshell. - The range of
#m_l# is based on the chosen#l# .

For example, since

#m_l = {-2,-1,0,+1,+2}#

That means five