Equations with meaning
Ψₙ₁ₘ(r, θ, φ) = Rₙ₁(r)Y₁ₘ(θ, φ)Every p orbital has angular quantum number ℓ = 1.
Probability density = |Ψ|²The square removes the positive/negative wavefunction sign.
Radial probability = r²|Rₙ₁(r)|²Probability in a thin spherical distance interval.
Radial nodes = n − 2Angular nodes = 1Total nodes = n − 1Eₙ = −13.6 eV / n²Hydrogen energy depends only on n in this simplified model.
For p orbitals, n begins at 2. The real px and py shapes are combinations of the complex mℓ = −1 and +1 states; pz corresponds to mℓ = 0 for the selected z axis.
Model boundaries
This is a one-electron, nonrelativistic hydrogen model. It is not a planetary atom, an electron path, or an exact model of a many-electron atom. Only the real Cartesian 2p and 3p orientation shapes are included.
The three-axis chamber, field coils, detector ring, nodal-plane sheet, and radial screen are illustrative teaching apparatus—not a calibrated instrument or direct photograph. Cloud points and measurement markers sample analytic hydrogenic probability densities.
Fine structure, Lamb shift, spin-orbit coupling, external-field splitting, electron-electron repulsion, shielding, hybridization, bonding, and time-dependent transitions are outside this simulation. One spatial p orbital may hold at most two opposite-spin electrons, but occupancy is shown only as a rule.