Homework Help: Probability Electron at Point: H Atom

1. Feb 2, 2014

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?

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2. Feb 2, 2014

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?

3. Feb 2, 2014

atomicpedals

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

4. Feb 2, 2014

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?