Probability Electron at Point: H Atom

[atomicpedals]

The problem I'm working on asks: At what radius does the probability of finding an electron at a point in the hydrogen atom fall to 50% of its maximum?

I've already worked through the problem to find the probability at the maximum, which was to take the first derivative of r^2 e^(-2r/a) and then set it equal to zero and solve for r (results in r = a). For the 50% of maximum do I simply set that derivative equal to 0.5? Sent from my iPad using Physics Forums

 

[BruceW]

ah, no that wouldn't get the right answer. the question is about probability. you have the wavefunction, so how do you calculate the probability of finding the electron at a certain place?

 

[atomicpedals]

Integral of the probability density; from 0 to 2pi in this case (I think).

 

[BruceW]

you don't need to do any integration. what's important is the probability density. if the probability of finding an electron in one place is 1/2 the probability of finding it in another specific place, then what can you say about the ratio of the probability density at these two points?