Atomic Orbitals & Shapes Simulation | Quantum Chemistry

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Concept Quiz

Quantum Mechanics & The Wavefunction

Electrons do not travel in perfectly circular orbits. Instead, their behavior is described by the Schrödinger equation. The solutions to this equation are wavefunctions ($\psi$). The square of the wavefunction ($|\psi|^2$) gives the probability density of finding an electron in a specific region of space—creating the 3D shapes we call orbitals.

$$ \hat{H} \psi = E \psi $$ $$ \psi_{n,l,m_l}(r, \theta, \phi) = R_{n,l}(r) \cdot Y_{l}^{m_l}(\theta, \phi) $$

$n$ = Principal Quantum No. (Energy / Size)
$l$ = Azimuthal Quantum No. (Shape: $s, p, d, f$)
$m_l$ = Magnetic Quantum No. (Spatial Orientation)
Phases (+/-): Represent the mathematical sign of the wavefunction, critical for molecular bonding (constructive vs. destructive interference).

Orbital Selection

Principal Quantum Number ($n$) n = 1 n = 2 n = 3 n = 4

Azimuthal Quantum Number ($l$) l = 0 (s-orbital)

Magnetic Quantum Number ($m_l$) m_l = 0 (s)

Positive Phase (+)

Negative Phase (-)

Quantum Structure

Orbital Name 1s

Max Electrons 2

Nodal Analysis

Angular Nodes ($l$) 0

Radial Nodes ($n-l-1$) 0

Total Nodes ($n-1$) 0

Nodes are regions where probability density $|\psi|^2 = 0$.

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