Where does the electron actually live? Solving the Schrödinger equation for hydrogen gives the orbitals — the glowing probability clouds that shape all of chemistry.
Hydrogen OrbitalsLive
electron probability clouds
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Solving the Schrödinger equation for hydrogen gives the orbitals — the probability clouds where an electron is likely to be found. The quantum numbers n, l, and m set the size, shape, and orientation. Brighter regions are higher probability density.
Reading this result: n=2 sets the shell and energy (E = -3.40 eV) and the overall size of the cloud. l=1 sets the shape: two lobes (p). m=0 sets the orientation in space. This orbital has 0 radial nodes and 1 angular node.
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How it works
The quantum numbers n, l, and m label hydrogen's orbitals and set their size, shape, and orientation. s orbitals are spherical, p orbitals form two lobes, d orbitals four — and the number of radial and angular nodes grows with n and l. These cross-sections of |ψ|² show where the electron is most likely to be found.
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The math, the assumptions, real-world uses, or a code translation — explained for this exact simulation.
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The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.