The orbital forms are actually representation of #(Psi)^2# all over the orbit streamlined by a contourOrbitals room actually bounded regions which describe an area wherein the electron deserve to be .Probability thickness of an electron is the exact same as #|psi|^2# or the square of wavefunction.

The wave function

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

where #R# is the radial component and #Y# is a spherical harmonic.#psi# is the product that two functions #R(r) and Y(theta,phi)# and thus it is directly attached to the angular and also radial nodes.And it is not surprising that the radial wave function and the angular wave role plot is various for each orbital since the wavefunction is various for every orbital.

For the hydrogen atom wavefunctions for various quantum values(which deserve to be assigned to different orbitals are )

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We recognize that for a 1s orbit in the hydrogen atom

#n=1,l=0,m=0#Therefore the the wavefunction is provided by

#Psi = <1/(ra_
color(white)()^3)>^0.5*e^(-p),p=r/(a_
)#

The wavefunction the the 1s orbital doesn"t has a angular component and also that can be easily figured out by the equation relenten it.Because angular component Y is dependent on #theta# for this reason it must be in the equation describing the wave functionFor part equations you may see the angular component like #cos theta or sin theta#

If you want a single function to explain all orbitals for the hydrogen atom then

#psi_(r,vartheta,varphi) = sqrt((2/(na_
))^3(((n-l-1))!)/(2n<(n+l)!>))e^-(rho/2)rho^lL_(n-l-1)^(2l+1)(rho)*Y_(lm)(vartheta,varphi)#

If r right here approaches #0# the limit of this function would it is in infinite#psi# is a product the #Y and also R# for this reason if you understand the wavefunction you deserve to easily find out the angular probability density

Different quantum numbers

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I"ll not enter this yet all this deserve to be deviated indigenous the Schrodinger equation for the hydrogen atom (for this image)

Now as soon as we recognize why the wavefunction is different for every orbital you can now analysis the plots

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Now there space some ups and down in the plot which are resulted in by nodes

What space nodes?

Wavefunctions room the options to the TISE. Mathematically these differential equations develop the nodes in the bound state wave functions, or orbitals. Nodes are the an ar where the electron probability thickness is 0.The two varieties of nodes room angular and radial. Radial nodes happen where the radial ingredient is 0