# The wave function of an orbital of H-Atom is given by: #psi=((sqrt q)/(81 sqrt pi))(1/a_0)^(3/2)(6-r/a_0)(r/a_0)e^(-r/(3a_0) )* sin theta sin phi# Then find the orbital ?

##
#1)# #2s#

#2)# #3p_y#

#3)# #3d_(z^2)#

#4)# #2p_x#

Is it the #2s# ???

Is it the

##### 1 Answer

There is no

**CHECKING THE ANGULAR NODES**

Furthermore, here's a relatively easy way to verify that you have a

This wave function given **goes to zero** when the *angular* component, which contains

When

**VERIFYING WHAT ORBITAL THIS BELONGS TO**

What you'll have to do is **separate** the wave function into its radial and angular components. This takes practice and you should reference your text to check if possible...

You gave:

#psi=((sqrt color(red)(q))/(81 sqrt pi))(1/a_0)^(3//2)(6-r/a_0)(r/a_0)e^(-r//3a_0 )* sin theta sin phi#

This **has** to be the

- It's the only wave function that contains
#sinthetasinphi# in its angular component. - It contains a
#(6 - r/a_0)# , unique to the#3p# radial wave function. - It contains an
#81# in its normalization constant, unique to atomic orbitals of#n = 3# .

But let's check if it matches...

The **actual 3py wave function** for a hydrogen-like atom is (*Inorganic Chemistry*, Miessler et al., 5th ed.):

#psi_(3,1,-1)(r,theta,phi)#

#= R_(31)(r) Y_(1)^(-1)(theta,phi)#

#= overbrace(1/(81sqrt3) ((2Z)/(a_0))^(3//2) (6 - (Zr)/(a_0))((Zr)/(a_0)) e^(-Zr//3a_0))^(R_(nl)(r) ("Radial")) cdot overbrace(1/2 sqrt(3/pi) sinthetasinphi)^(Y_(l)^(m_l)(theta,phi)("Angular"))#

For hydrogen atom then,

#= overbrace((cancel(2)cdot sqrt2)/(81cancel(sqrt3)) ((1)/(a_0))^(3//2) (6 - (r)/(a_0))((r)/(a_0)) e^(-r//3a_0))^(R_(nl)(r) ("Radial")) cdot overbrace(1/cancel(2) sqrt(cancel(3)/pi) sinthetasinphi)^(Y_(l)^(m_l)(theta,phi)("Angular"))#

#= color(blue)(overbrace(sqrt2/(81 sqrt(pi)) (1/(a_0))^(3//2) (6 - (r)/(a_0))((r)/(a_0)) e^(-r//3a_0))^(R_(nl)(r) ("Radial")) cdot overbrace(sinthetasinphi)^(Y_(l)^(m_l)(theta,phi)("Angular"))#

I didn't change anything; all I did was take two already-separated components from my textbook, combine them together, and cancel out terms that have ratios of

It's the same wave function that I first referenced, and evidently, this matches the