Probability that the electron is found at a distance greater than r

  • #1
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The problem given is to calculate the probability that the electron is found at a distance greater than r=2a0 from the center of the hydrogen atom in its ground state.

I don't understand what the problem is asking. I don't understand what form of the wavefunction I should use.

I know that to calculate the probability is P(r)= abs value (ψ(r))^2 or P(r)= ψ*(r).ψ(r)

but what wave function should i use in this problem? should i use e^(r/a0)/sqrt(pi.a0)?

i know that at the ground state n=1 in which makes n,l=0
 
  • #2
Just take the ground state wavefunction and integrate the square from 2a0 to infinity, [itex] P(r>2a_0) =\int_{2a_0}^\infty \psi^*(r) \psi (r) dr[/itex]
 
  • #3
Thank you!
 
  • #4
I have a question, in order to solve the same problem but if we use the wave function of the Radial functions of the Hydrogen atom is $$R10= 2/(sqrt(a0^3))*e^(-r/a0)$$ ?
 
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