Visualise hydrogen atom electron orbitals as 3D probability clouds. Select quantum numbers (n, l, m) to see s, p, d and f orbital shapes — the fundamental building blocks of chemistry.
The hydrogen wavefunction ψ(n,l,m) is computed from spherical harmonics and radial functions. Point density represents |ψ|² — the probability of finding the electron.
Select quantum numbers n (1-4), l (0 to n-1) and m (-l to l). Watch the orbital shape change. Rotate to view from different angles.
Electron orbitals explain the periodic table's structure. The s, p, d, f naming comes from spectroscopic observations: sharp, principal, diffuse, fundamental — terms from the 1890s.
This visualiser renders the electron probability density of a single hydrogen atom as a luminous 2D cross-section through the 3D orbital. For your chosen quantum numbers it evaluates the analytic wavefunction ψ(n, l, m) — a radial part built from associated Laguerre polynomials multiplied by a real spherical harmonic from associated Legendre polynomials — and plots |ψ|², the chance of finding the electron at each point. The result reveals the s, p, d and f orbital shapes that underpin all of chemistry.
It samples the exact hydrogen wavefunction on a plane and colours each pixel by |ψ|². The radial factor R(n,l) uses associated Laguerre polynomials in units of the Bohr radius, while the angular factor uses real spherical harmonics (cosine for m greater than 0, sine for m less than 0). Dashed axes and faint yellow n²·a₀ shell rings give scale.
Drag the n (1-5), l (0 to n-1) and m (-l to l) sliders, which auto-clamp to physically allowed values, or hit the 1s, 2p, 3d and 4f preset buttons. The Threshold slider (1-50%) hides low-density haze, and the Slice menu picks the XZ, XY or YZ cross-section plane. A pill label shows the current orbital name.
Hydrogen is the only atom whose Schrödinger equation can be solved exactly in closed form. The s, p, d, f labels are not arbitrary: they come from 1890s spectroscopy, standing for sharp, principal, diffuse and fundamental spectral series.
You are seeing a flat slice through the three-dimensional electron probability cloud of a hydrogen atom. The brightness at every point is proportional to |ψ|², the probability density of finding the single electron there. Bright regions are where the electron is most likely to be; dark regions are nodes or low-probability space.
The simulation evaluates the exact analytic solution of the hydrogen Schrödinger equation. The radial part R(n,l) uses an associated Laguerre polynomial with an exponential decay, expressed in Bohr radii. The angular part uses an associated Legendre polynomial combined into a real spherical harmonic, with cosine(mφ) for positive m and sine(|m|φ) for negative m.
They are the three quantum numbers that define an orbital. The principal number n (1-5) sets the energy and overall size, the azimuthal number l (0 to n-1) sets the shape (s, p, d, f), and the magnetic number m (-l to l) sets the orientation. The sliders automatically restrict l and m to the values physics permits for each n.
Yes, the maths is the genuine textbook hydrogen solution rather than an artistic impression. The chief approximation is that it shows a single 2D slice and normalises brightness per frame, and it uses the real (cosine/sine) spherical harmonics commonly drawn in chemistry rather than the complex eigenstates, so shapes match standard orbital diagrams.
Nodes are surfaces where ψ passes through zero, so the probability of finding the electron there is exactly nil. An orbital has n-1 total nodes, split between radial nodes (concentric shells) and angular nodes (planes or cones). These standing-wave patterns arise because the electron behaves as a wave confined by the proton's attraction, much like the harmonics of a vibrating object.