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# Radial Wave Function of Hydrogen

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Use the Radial Wave Function of a Hydrogen-like atom to calculate the radii of the 2 nodes of the 3s orbital in units of a0 for the H atom.

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Use the Radial Wave Function of a Hydrogen-like atom to calculate the radii of ...

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The solution shows how to use the radial wave function for hydrogen to calculate the radius.

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## Hydrogen atom - radial wave function normalization

R(r)=Nr^l e^(-Zr/na) ∑_(j=0)^(n-l-1)▒〖b_j r_j 〗
Finding the normalization constant:
Rodriguez formula for associated Laguerre formula is:
(e^x x^(-k))/n! d^n/(dx^n ) (〖e 〗^(-x) x^(n+k) )=(e^x x^(-k-n))/n! x^n d^n/(dx^n ) (〖e 〗^(-x) x^(n+k) )
R(r)=∫_0^∞▒(Nr^l e^(-Zr/na) (e^x x^(-k-n))/n! x^n d^n/(dx^n ) (〖e 〗^(-x) x^(n+k) ))^2 dr=1 (a)

Can you find N for me by using the formula for R(l) in (a)

Answer is in the purple box:

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