Electronic distribution of hydrogen (chart) Calculator

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Calculates a table of the electron radial distribution of hydrogen-like atoms and draws the chart.

The electron position r with the Bohr radius a = 1 unit is the distance from the nucleus.

\(\normalsize Probability\ density\ of\ finding\\
\hspace{50px}\ electron\ in\ a\ Hydrogen\ atom\\
(1)\ -{\large\frac{\hbar^2}{2m}}\nabla^2\psi-{\large\frac{Ze^2}{r}}\psi=E\psi\\
\hspace{30px}E=-{\large\frac{Z^2me^4}{2n^2\hbar^2}}, Z=\{1:H,\ 2:He^+\}\\
\hspace{30px}\psi_{n,l,m}(r,\theta,\phi)=R_{nl}(r)Y_l^{m}(\theta,\phi)\\
(2)\ R_{nl}(r)=-\sqrt{({\large\frac{2Z}{na}})^3{\large\frac{(n-l-1)!}{2n(n+l)!}}}e^{-{\normalsize\frac{Zr}{na}}} \\
\hspace{90px}\times\ ({\large\frac{2Zr}{na}})^{l} L_{\small{n-l-1}}^{\small{2l+1}}({\large\frac{2Zr}{na}})\\
\hspace{30px}a={\large\frac{\hbar^2}{me^2}}\ :Bohr\ radius\\
(3)\ Probability\ density:\ R_{nl}(r)R_{nl}^*(r)r^2\\
\hspace{20px}{\large\int_{\small 0}^{\small{\infty}}}R_{nl}R_{nl}^*(r)r^2dr=1\\\)

Electronic distribution of hydrogen (chart) Calculator

Calculates a table of the electron radial distribution of hydrogen-like atoms and draws the chart.

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Electronic distribution of hydrogen (chart) Calculator

Calculates a table of the electron radial distribution of hydrogen-like atoms and draws the chart.

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History

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