Does the hydrogen atom 'expand' or 'contract' when an electron is excited from the n = 1 state to the n = 3 state?

Question

Accepted Answer

hey everyone in this example, we need to determine whether the excitation of an electron from the second energy level to the fifth energy level will either expand or contract the hydrogen atom. So we should visualize a hydrogen atom and specifically its nucleus which is in the center and filled with densely packed positively charged protons. And then because the prompt says we begin with our electron at the second energy level, we're going to draw our energy levels with these circles here. So this is the first energy level. Now we have the second energy level where are electron is located. And according to the prompt, this electron is excited up to the fifth energy level. So we're going to draw three more circles for the fifth energy level. Right now we're drawing the third energy level. This is our 4th energy level. And then now our electron ends up at this last energy level, which is our fifth energy level. So we would say that this energy level is And equals five and initially our electrons that n equals two. So it gets excited up to the 5th energy level. So as you can see what has occurred here is now we have a distance that is farther from our nucleus of our hydrogen atom to our electron now at the fifth energy level. This distance is a much larger distance compared to the distance where our electron was at the second energy level, which is a smaller distance here, which we can also just go ahead and draw in. So that would be the electron being here compared to the nucleus. And so what we should recall is our concept of effective nuclear charge, which is describing the distance between our electrons in our outer show and our protons in our atoms nucleus. And specifically effective nuclear charge is describing the pull that are protons in our nucleus have on the electrons in our outer shells here. Based on how far or close they are. That poll will either weekend or get stronger. So because we say that the distance increases at the transition of N equals two to n equals five. So the electron ending up at the fifth energy level. So the distance increases so therefore now because we have a greater distance between our protons and our electrons. The pull that these protons in our nucleus have on this electron here at the fifth energy level is now at a farther distance. And so our effective nuclear charge is going to decrease. And so we can confirm that thus due to this effective nuclear charge decreasing our hydrogen adam well expand. So in other words, the atomic radius of a hydrogen atom is going to increase in size. And that is also due to the fact that the probability of finding an electron now at the fifth energy level is going to increase due to the greater volume of distance between our proton and our nucleus to our electron at the fifth energy level. And so our final answer is that our hydrogen atom is going to expand based on the increase in distance and decrease in our effective nuclear charge between our protons and our nucleus, to the electrons at the fifth energy level. Now, so this is our final answer. I hope that everything I went through is clear. If you have any questions, please leave them down below, and I will see everyone in the next practice video.

Does the hydrogen atom 'expand' or 'contract' when an electron is excited from the n = 1 state to the n = 3 state?

Verified Solution

Key Concepts

Quantum States

Electron Excitation

Atomic Radius