# Solving a Wavefunction

Question: What is the complete wavefunction for n=2, L=0, and m(sub L)= 0? What radius of the orbital specified is required to contain 95% probability of finding an electron?

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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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