Question Video: Determining the Distance from the Nucleus at Which an Electron in a 1s Orbital is Most Likely to be Found | Nagwa Question Video: Determining the Distance from the Nucleus at Which an Electron in a 1s Orbital is Most Likely to be Found | Nagwa

Question Video: Determining the Distance from the Nucleus at Which an Electron in a 1s Orbital is Most Likely to be Found Chemistry • Second Year of Secondary School

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The graph shows the probability of finding the electron at a distance from the nucleus in the 1s orbital of an atom of hydrogen. At what approximate distance is the electron most likely to be found from the nucleus?

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Video Transcript

The graph shows the probability of finding the electron at a distance from the nucleus in the 1s orbital of an atom of hydrogen. At what approximate distance is the electron most likely to be found from the nucleus?

Here is the graph. The probability of finding the electron is on the 𝑦-axis, and its distance from the nucleus is on the 𝑥-axis. Without units for the probability axis, we can assume we’re dealing with relative probability. So points that are higher up the 𝑦-axis have a higher probability than points that are lower. The question also tells us we’re dealing with an electron in the 1s orbital of an atom of hydrogen. An atom of hydrogen has the electron configuration 1s1. s-type orbitals are spherical. This means the probability of finding an electron doesn’t vary depending on which angle you’re pointing out. It’s only the distance from the nucleus that matters.

We need to find the approximate distance from the nucleus of this electron that’s most likely. The most likely event is the one with the highest relative probability. So we need to find the highest point of this curve and then draw down to the 𝑥-axis to find the distance. The highest point on this curve is here. This corresponds with a distance from the nucleus the 50 picometers. The question is only asking for the approximate distance. But to my eye, that peak is bang on the line of 50 picometers, so we can be comfortable that 50 picometers is the correct answer. What this means is if you were to check where the electron was in a 1s orbital of a hydrogen atom, more times than any other it would be in about 50 picometers.

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