Finding the probability (again)

[NicolasM]

So, we have a hydrogen atom. What is the probability of an electron being found in a spherical shell with 0,01Å width and a radious of 0,35Å?

By approximation, we can sonsider the value of ψ (1s) stable within the shell, and thus the chance is ψ² x Volume. Right?
Also, by considering 0,35Å the median radious, can I express the probability as _0,345∫^0,355 ₀∫^2π ₀∫^2π ψ² r² sineφ dr dφ dθ ? Would that give a more accurate solution?

 

[Simon Bridge]

the chance is ψ2 x Volume

... you mean:

The probability of finding a particle with wave-function $\psi$ in volume $V$ is $$P_V=\int_V \psi^\star\psi \; dv$$

Also, by considering 0,35Å the median radious, can I express the probability as 0,345∫0,355 0∫2π 0∫2π ψ2 r2 sineφ dr dφ dθ ? Would that give a more accurate solution?

That would be reasonable taking the "radius" as the center of the shell.
Don't forget that the 1s shell has angular as well as radial components, something like: ... $\psi=Y(\theta,\phi)R(r)$.

You can use the symmetry of the 1s state to work out the result of the integration over all possible angles. It may help to measure radii in units of the Bohr radius.