Atomic Orbitals 3D Viewer
Equations in this simulation
| n | principal quantum number | the shell: 1, 2, 3 or 4 here; it sets the energy and the size | |
|---|---|---|---|
| Z | Nuclear charge Z (1 for hydrogen; higher for a one-electron ion) | with one electron, the energy depends on n alone, not on l | |
| E | energy of the orbital | zero is the electron pulled right away from the nucleus; −13.6 eV for hydrogen's 1s |
With the current values:
| l | angular momentum quantum number | 0 = s, 1 = p, 2 = d, 3 = f; it sets the shape | |
|---|---|---|---|
| m_l | magnetic quantum number | from −l to +l; the real x, y, z orbitals shown are combinations of +m and −m, so only |m_l| is fixed | |
| nodes | surfaces where the electron is never found | radial nodes are spheres, angular nodes are planes or cones through the nucleus; n − 1 in all |
With the current values:
| P(r) | radial distribution | the chance of finding the electron at distance r, over all directions; the chart plots it | |
|---|---|---|---|
| a₀ | Bohr radius | 52.9 pm, the most likely distance of the 1s electron in hydrogen | |
| r_mp | most probable distance | the highest peak of P(r) |
With the current values:
| ⟨r⟩ | average distance from the nucleus | the running average of the measured positions settles on it |
|---|
With the current values:
| configuration | Element for the electron configuration (atomic number) | filled in the order 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p, with Hund's rule inside each subshell and the known exceptions such as chromium and copper |
|---|
With the current values:
How to use the atomic orbitals viewer
- Pick an orbital. Each point in the cloud is a place the electron could be found, drawn from the hydrogen wavefunction, so the cloud is dense where the electron is likely and thin where it is not. Blue and orange show the sign (phase) of the wavefunction, which matters when orbitals overlap to form bonds.
- Tick Cut away the front half to see inside: the 2s, 3s and 4s orbitals hide spherical nodes, shells where the electron is never found, which show on the chart of the radial distribution as gaps between the peaks. The white flash is a single measurement of the electron's position; the chart over time shows the measured distances and their running average settling on ⟨r⟩.
- Raise the nuclear charge to see the orbital shrink as 1 ÷ Z for a one-electron ion such as He⁺ or Li²⁺, and move the element slider to get the electron configuration of any element up to xenon, with the count of unpaired electrons by Hund's rule. The Bohr Atom Simulator shows the older planetary model and the spectral lines.
Frequently asked questions
What is an atomic orbital?
A wavefunction that describes where an electron in an atom is likely to be found. Its square gives the probability density, so an orbital is not a path but a cloud of probability. Each orbital holds at most two electrons, with opposite spins. Its shape is set by the quantum numbers: n the size and energy, l the shape (s, p, d, f), and m_l the orientation.
Why do p orbitals have two lobes?
The angular part of a p orbital is proportional to x, y or z, which is positive on one side of the nucleus and negative on the other, and zero on the plane between them. That plane is an angular node. The two lobes have opposite phase, shown here in blue and orange; the electron is equally likely in either lobe and never on the nodal plane.
What are radial and angular nodes?
Surfaces where the wavefunction is zero. An orbital has n − 1 nodes in all: l angular nodes (planes or cones through the nucleus) and n − l − 1 radial nodes (spheres). So 1s has none, 2s one sphere, 2p one plane, 3d two angular nodes, and 4f three.
Why does 4s fill before 3d?
In many-electron atoms the inner electrons screen the nucleus, and an s electron, which spends part of its time very close to the nucleus, is screened less than a d electron. That lowers 4s just below 3d for potassium and calcium. Once the 3d orbitals start filling they drop below 4s again, which is why transition metals lose their 4s electrons first when they form ions, and why chromium and copper take 3d⁵ 4s¹ and 3d¹⁰ 4s¹.
It says WebGL is turned off.
The 3D view needs WebGL, which every current browser has. It can be switched off by hardware acceleration being disabled in the browser settings, or by a very old graphics driver. Turn hardware acceleration on, or try another browser.
Is anything uploaded?
No. The simulation is drawn by your own browser with WebGL; nothing is sent anywhere, and it keeps working offline once the page has loaded.