Collect independent simulated position measurements from identically prepared hydrogen 1s states. The accumulation forms a spherical probability cloud; a movable radius gate compares measured counts with the exact radial probability.
• A hydrogen nucleus, independent position outcomes, a spherical probability gate, a central slice indicator and a radial probability profile. • Controls for the radius gate (Bohr radii a₀), measurements per second, a repeatable sampling seed and a thin central slice. • Four tabs: Observatory, Geometry & measurements, Experiments (with built-in model checks), and Learn & assess.
|ψ1s|² = exp(−2r/a₀)/(πa₀³); with x = r/a₀ the radial PDF is p(x) = 4x² exp(−2x). P(r < R) = 1 − exp(−2X)(1 + 2X + 2X²) with X = R/a₀. The mean radius is 1.5a₀ and the most probable radial distance is a₀. Samples use x = −½ ln(U1 U2 U3) with an isotropic direction.
This is nonrelativistic hydrogen 1s only. It samples position statistics from repeated identically prepared atoms; it is not electron motion, a wavefunction-collapse time model or a many-electron atom. The sample cap is 4,000, the nuclear size is enlarged, and the slice affects displayed dots only.
No. They are independent measurements on identically prepared states.
No. Shell-volume weighting makes the 1s radial PDF peak at a₀, even though the probability density itself is highest at the nucleus.
About 32.3% of measurements lie inside a₀ and about 93.8% lie inside 3a₀; sample estimates fluctuate around these exact values.
It covers nonrelativistic hydrogen 1s only, with a 4,000-sample cap and an enlarged nucleus; it is not electron motion, a collapse-time model or a many-electron atom.