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Chapter 8: Problem 56

The greatest probability of finding the electron in a small-volume element of the 1 s orbital of the hydrogen atom is at the nucleus. Yet the most probable distance of the electron from the nucleus is \(53 \mathrm{pm}\). How can you reconcile these two statements?

Short Answer

Expert verified
The biggest probability of finding the electron in a small volume is at the nucleus because this is where the electron’s probability density is the greatest due to the shape of the s orbital. However, the most probable distance is 53pm because, considering all the possible positions for the electron within the 1s orbital, it has a higher probability to be found somewhere in that volume around the nucleus than exactly at the nucleus.

Step by step solution

01

Understanding atomic orbitals

Atomic orbitals (like the 1s orbital in the hydrogen atom) can be thought of as regions in an atom where an electron is most likely to be found. The 1s orbital is the closest to the nucleus and, being spherically symmetrical, has the highest electron density near the nucleus
02

Define Electron Probability Density

Electron probability density refers to the likelihood of finding an electron in a particular region of an orbital. For the 1s orbital of a hydrogen atom, the electron probability density is maximum at the nucleus. This means that any small-volume element you choose at the nucleus will have the highest chance of containing the electron.
03

Explain the most probable distance

The most probable distance is where the electron can be found most of the time, considering all the possible positions in the 1s orbital. Because the electron has the whole volume of the orbital at its disposal, and due to the spherical nature of the 1s orbital, finding the electron exactly at the nucleus (a point) is actually less probable than finding it somewhere within the sphere of the orbital. This is why the most probable distance of the electron from the nucleus is not zero but \(53 \mathrm{pm}\) for a hydrogen atom.

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