(d) For the hydrogen atom, list the following orbitals in order of increasing energy: 3s, 2s, 2p, 5s, 4d.

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Welcome back everyone in this example, we need to arrange the orbital's of a helium plus one atom. In order of decreasing energy according to the given sub shells being one S, two S, two, P three S and three D. We're told to use the equal symbol for equal energy level orbital's. So we want to recall something known as our principal quantum number. Recall that that is describing the term N. Where N represents our energy level where our electron of our atom and we can say electrons of our atom reside. So looking at the prompt according to the given sub shells, we go all the way up to the third energy level where our helium kati on electrons could potentially be located at. Recall that our principal quantum number includes positive integers only up to infinity. So the principle quantum number lends us varying probabilities of electron occupation in different energy levels. Now when we think of uncharged helium which is just neutral helium H E without a charge, we want to recall that its ground state configuration is going to be one S two. But in this case according to the pump were given helium as a charged catalon. And recall that acadian charge means we will lose that number of electrons. So we would have a ground state configuration That's one S 1 since we lose one electron. Now because we should recall that helium as a gas, we would say that therefore to get to an excited state configuration, we would shine light on our helium adam Or in this case our 80 plus Adam. And so recall that on our electromagnetic spectrum energy increases towards the direction of X rays. So we could shine UV light visible light or x rays on our helium atom to get it to be excited so that its electrons have the potential to be moved up to higher energy levels or higher principle quantum numbers. But again, helium only has two electrons when it's neutral. And our ground state charged atom of helium with a plus one charge has just one electron. And so this one electron can be excited up to the two S two P three S or three D orbital's or sub shells where we could say that are excited. Helium catalon configuration could be something like two S one or two P one or three S one Or three D 1. And we're going to stop at three D one because recall that again, according to our electromagnetic spectrum energy increases towards the direction where X rays are, which is on the left hand portion of our electromagnetic spectrum, meaning that we only still have a limited amount of energy based on the energy capacity of the type of light that we shine on our helium gas. And since we understand that the energy level of our sub shells is represented by our principal quantum number N, which are are positive integers of our sub shells given in the prompt here. We're going to rank them based on these values. And so in order of decreasing energy, we would say that we can rank our sub shells slash orbital's by decreasing energy where we would have equal and values for the D. And S. Sub shell because they both have a three in front of them. So we would say that our three D. Sub shell is equivalent to R three S. Sub shell where our three s. Sub shell has a higher principle quantum number being the value three here than R two S. Sub shell. So we would say it's greater in energy than R two S. Sub shell which is then equal to the amount of energy in our two P sub shell. And again because R two P sub shell has a principal quantum number of two, it has more energy than our ground state configuration of our helium catalon which is one. S. And so this ranking here is our ranking of our sub shells and orbital's of our helium Catalan in order of decreasing energy. So we have the lowest energy associated with our one s. Sub shell here of our helium caddy on. So it's highlighted in Yellow completes this example as our final answer. I hope everything that I reviewed was clear. If you have any questions, please leave them down below and I'll see everyone in the next practice video

(d) For the hydrogen atom, list the following orbitals in order of increasing energy: 3s, 2s, 2p, 5s, 4d.

Verified Solution

Key Concepts

Quantum Numbers

Aufbau Principle

Energy Levels and Sublevels