Quantum Mechanics / Uncertainty Principle Question

[fazer2014]

Homework Statement

The square of a wave function gives the probability of finding a particle at a given point. What is the probability of finding an electron in a 1s orbital within a volume of 1pm^3, centred at:
a) the nucleus
b) 50pm away from the nucleus?

Homework Equations

Heisenberg Uncertainty Principle

The Attempt at a Solution

I sense that this is actually a straightforward question, but I just can't get my head around what it's asking. I feel like the first sentence is not actually relevant to solving the question, just a little ditty of information? I'm also thrown by the 'centred at' thing. If anyone can offer an explanation for how to think about this problem it would be greatly appreciated, thanks.
(Sorry, this is actually for a chemistry class, but I searched the forums and there are a few questions on this topic, though none I could find that answered this specific question).

 

[nrqed]

Homework Statement

The square of a wave function gives the probability of finding a particle at a given point. What is the probability of finding an electron in a 1s orbital within a volume of 1pm^3, centred at:
a) the nucleus
b) 50pm away from the nucleus?

Homework Equations

Heisenberg Uncertainty Principle

The Attempt at a Solution

I sense that this is actually a straightforward question, but I just can't get my head around what it's asking. I feel like the first sentence is not actually relevant to solving the question, just a little ditty of information? I'm also thrown by the 'centred at' thing. If anyone can offer an explanation for how to think about this problem it would be greatly appreciated, thanks.
(Sorry, this is actually for a chemistry class, but I searched the forums and there are a few questions on this topic, though none I could find that answered this specific question).

It is not really an uncertainty question.

First, note that the probability is not given by the square of the wave function! The probability of finding the particle in a small volume $dV$ is actually given by

$$\bigl| \psi (r, \theta, \phi) \bigr|^2 \, dV$$

So just square the wave function at the values of r given in the questions and multiply by the small volume.

 

[fazer2014]

I see... thanks, I understand in theory. But we weren't actually given a wave function. So is it just a thought experiment or something?

 

[Orodruin]

You were given the state (1s orbital). I suggest looking up the wave function for the ground state in a hydrogen-like potential.