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

1. Nov 22, 2011

### hansbahia

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 dont 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. Nov 22, 2011

### cbetanco

Just take the ground state wavefunction and integrate the square from 2a0 to infinity, $P(r>2a_0) =\int_{2a_0}^\infty \psi^*(r) \psi (r) dr$

3. Dec 19, 2011

### hansbahia

Thank you!

4. Nov 19, 2013

### exp626n64

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 $$R10= 2/(sqrt(a0^3))*e^(-r/a0)$$ ?

Last edited: Nov 19, 2013