An electron orbital is a three-dimensional region around an atom's nucleus where an electron has the highest probability (typically ~90–95%) of being found. Unlike the outdated Bohr model that depicts electrons in fixed circular "orbits," quantum mechanics describes orbitals as probability clouds defined by wave functions. Each orbital is characterized by three quantum numbers: n (principal, determines size/energy), l (angular momentum, determines shape), and m (magnetic, determines orientation).

s orbitals (l=0) are spherical — perfectly symmetric around the nucleus. p orbitals (l=1) have a dumbbell or figure-8 shape with two lobes on opposite sides of the nucleus (along x, y, or z axes). d orbitals (l=2) mostly have a four-lobed cloverleaf shape (except d_z², which has two lobes plus a donut-like ring). f orbitals (l=3) exhibit complex multi-lobed shapes with up to eight lobes arranged in intricate three-dimensional patterns.

n (Principal Quantum Number): Determines the energy level and average distance from the nucleus. n = 1, 2, 3, ... Higher n means the electron is farther out and has higher energy.
l (Angular Momentum Quantum Number): Defines the orbital shape. l ranges from 0 to n−1. l=0→s, l=1→p, l=2→d, l=3→f.
m (Magnetic Quantum Number): Specifies the orbital's spatial orientation. m ranges from −l to +l. For p orbitals (l=1), m = −1, 0, +1 correspond to p_x, p_z, p_y orientations.

The electron cloud in this tool is generated using Monte Carlo rejection sampling based on hydrogen-like atomic wave functions. We randomly sample points in 3D space and accept them with probability proportional to |ψ(r,θ,φ)|² — the probability density derived from the product of the radial function R_nl(r) and the real spherical harmonic Y_lm(θ,φ). The resulting point cloud reflects where electrons are most likely to be found, with denser regions indicating higher probability.

An orbit (from the Bohr model, 1913) is a fixed, well-defined circular path where electrons were thought to revolve around the nucleus — like planets around the Sun. An orbital (from quantum mechanics, 1926) is a probability distribution: a 3D region where an electron is most likely to be found, with no defined path. Orbits are deterministic; orbitals are probabilistic. Modern chemistry relies entirely on the orbital model.

Yes! Radial nodes (spherical shells where probability drops to zero) and angular nodes (planes or cones where probability vanishes) are naturally visible as gaps or sparse regions in the electron cloud. For example, the 2s orbital has one radial node (a dark spherical gap), while p orbitals have an angular node at the xy, xz, or yz plane (the "waist" of the dumbbell). Switch between orbitals to observe these features.

The complexity arises from higher angular momentum (l=2 for d, l=3 for f). The spherical harmonic functions Y_lm(θ,φ) for higher l values have more angular nodes and more intricate directional dependence. d orbitals feature four lobes (with alternating phase signs) due to the sin²θ·cos(2φ) and similar patterns in their wave functions. f orbitals (l=3) have up to eight lobes because the spherical harmonics involve cubic combinations of x, y, z coordinates, creating even more intricate three-dimensional patterns.

Rotate: Click and drag with your mouse or finger to rotate the orbital in 3D.
Zoom: Use the scroll wheel or pinch gesture to zoom in/out.
Pan: Right-click and drag (or two-finger drag on mobile) to pan the view.
Switch orbitals: Use the dropdown menu or control panel to explore different orbital types.
Toggle views: Switch between Cloud (probability dots), Surface (solid isosurface), or Both modes.
Auto-rotate: Enable auto-rotation for a dynamic 360° view — great for presentations and teaching.