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## Homework Statement

How to calculate the probability of finding an 1s electron within 1 picometer cubic region located 50pm from the nucleus.

## Homework Equations

The probability of an 1s electron within a spherical volume of radius 'a' from nucleus can be find using the expression

$$\int_{0}^{a}\int_{0}^{\pi}\int_{0}^{2\pi}|\psi(r,,\theta,\phi)|^2r^2 dr \sin(\theta) d\theta d\phi$$

but how to find probability within a cubic region?

## The Attempt at a Solution

I thought I could transform ${(r,\theta,\phi)}$ into (x,y,z) coordinates and integrate the above integral within proper limits, but the integral will become messy! and also I don't know whether it is the proper way of doing this problem, all I am asking is give me a hint how to do this problem?