[Mark S 2014]

Given the radial wavefunction of the hydrogen 2s orbital, what is the probability of finding the electron in a small volume of 1 pm³ ?

Is this equal to the square of the wavefunction multiplied by the volume, i.e ψ² × (1×10^-12 m³ ?

I can't find anything in my notes or my textbook about this

[Mark S 2014]

Sorry, forgot to add that this what for a distance of 52.9 pm from the nucleus !

[Corribus]

First, you need to know how you find the probability of finding a particle between r and dr using the radial probability distribution for hydrogen 1S orbital. Then you need to know what the appropriate integration limits are for your problem. (I.e., determine what radius is equal to a sphere volume of 1 pm³, then integrate between 0 and that number).

[Mark S 2014]

Thanks corribus, so is that P(r) = 4πr²R(r)² for the radial distribution function ?

[Corribus]

Yes!

http://chemwiki.ucdavis.edu/Physical_Chemistry/Quantum_Mechanics/Quantum_States_of_Atoms_and_Molecules/8._The_Hydrogen_Atom/The_Wavefunctions

[mjc123]

That's not how I read the question. I take it as a volume element of 1 pm³ at a distance of a₀ - not a sphere of volume 1 pm³ centred at the nucleus. I think the original answer is correct, P = Ψ²dv, where Ψ is the value of the wavefunction at a₀.