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I'm having a bit of trouble with solving the following problems, so help would be appreciated a lot!

Consider a hydrogen atom in the ground state. Calculate the relative probability of finding the electron in the area described:

a) In a sphere of volume 1.0 E^{-3}pm^{3}centered at the nucleus

Well this wasn't really hard: the volume is 1.0 E^{-3}pm^{3}= the volume of a sphere = 4/3 pi r^{3}.

Dividing by 4/3 pi and taking the 3-rd square root gave me r= 0.0620350491 E^{-12}m.

The psi^{2}function of the 1s orbital is:

(1/pi) (1/a_{0})^3 e^{-2r/a0}

The radial probability distribution is obtained when the function above is multiplied with the formula for the surface of a sphere given by 4 pi r^{2}. Integrating between 0 and the radius 0.0620350491 E^{-12}m gives a probability of 2.2E^{-9}.

Now the hardest part. I don't know how to get to a right answer with these questions:

Calculate the relative probability of finding the electron in the area described:

b) In a sphere of volume 1.0 E^{-3}pm^{3}centered on a point 1.0 E^{-11}m from the nucleus.

c) In a sphere of volume 1.0 E^{-3}pm^{3}centered on a point 53 pm from the nucleus.

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# Homework Help: QM- Relative probability of finding an electron

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