[LucaZombini]

"on page 60 it is affirmed that the maximum probability to find the 1s electron of the hydrogen atom is on the nucleus. on the same page it is also affirmed that the maximum probabiliy to find the electron is at 53 pm of distance from the nucleus. why are both of the previous affirmations correct?"

[Borek]

1. You have to show your attempts at answering the question to get help, this is a forum policy.

2. Have you read the page 60? What does it say about both statements? What equations are used to calculate both probabilities?

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[LucaZombini]

it says that in a spheric shell with dR as thickness and volume 4πr² ψ² dr the probability to find the electron is the highest at a distance of 53 pm from the nucleus and decreases with the distance but the first statement says that the density is the highest on the nucleus.

[Corribus]

It would be better to see the actual text or for you to reproduce what the textbook actually says.

However - while the radial wavefunction has a maximum value at the nucleus (r = 0), the probability distribution function in spherical coordinates is the product of the wavefunction squared and r^2, which for the 1S orbital has a value of zero at the nucleus (and a maximum value related to the bohr radius and the nuclear charge).