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Ψ-co(The Atoms’ Motel)

Introduction:Over the course of several years, I have tried to find

an appropriate analogy which would describe the way in which the electrons occupy their respective positions in an atom. I tried various methods – from straight physical/chemical descriptions to parking garage analogies – and still never seemed to get the point across or lost student interest at the first mention that “each energy level contains the same number of sublevels as the number of the principle level.” I saw that a different approach was warranted. Thus, the “Atoms’ Motel” was designed and ‘built.’

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Ψ-co(The Atoms’ Motel)

Introduction:Over the course of several years, I have tried to find

an appropriate analogy which would describe the way in which the electrons occupy their respective positions in an atom. I tried various methods – from straight physical/chemical descriptions to parking garage analogies – and still never seemed to get the point across or lost student interest at the first mention that “each energy level contains the same number of sublevels as the number of the principle level.” I saw that a different approach was warranted. Thus, the “Atoms’ Motel” was designed and ‘built.’

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Ψ-co (The Atoms’ Motel)

The Motel:Deep in the depths of the atomic realm, there exists a haven for the wayward

and weary electron traveler: the Atoms’ Motel. It is not a plush resort, but very serviceable, discrete, and distinctively stylish. It has a lobby containing the check-in desk, a very attractive German restaurant, and an electronic game room. There is no pool; electrons can get shorted out when in water. Electrons occupy the motel with great frequency and will take quantum leaps to get there.

Above the ground level lobby, there are seven levels of rooms, each having its own style and décor. The first level, for example, has only one room, a suite with only one double bed. It is the first priority for traveling electrons due to its nearness to the ground level and its ample amenities. If fact, lower level rooms are extremely popular to electrons; they want to expend the least amount of energy necessary to get to their rooms, and, by the way, they are not at all bashful about sharing their accommodations with fellow electrons in order to occupy these key locations.

The second level has a total of two rooms – one suite with one double bed and one party room with three (3) double beds. The third level differs from the second in that it consists of three rooms – a suite with one double bed, a party room with three double beds, and, in addition, one dormitory room with five (5) double beds. Odd, is it not? The third floor suite is just ever so slightly further from the ground level than the previous level’s party room.

When electrons get to the fourth level, things change a bit more. There is the one suite with one double bed, one party room with three double beds, one dorm room with five double beds, and, now, an additional faraway room with seven (7) double beds. Odder still! On level four, the suite is slightly farther from the ground level than the third level party room, but closer than the dorm room and its five beds.

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Ψ-co (The Atoms’ Motel)

The fifth level is exactly like the fourth, but some day, hopefully, there will be enough electron demand to add a fifth room with nine (9) double beds to level five. Gee!

Since the motel is still under construction, the sixth and seventh levels have only a few rooms completed. The sixth has only the suite, party, and dorm rooms complete, while the seventh level has only the suite.

Registration:When a traveling electron arrives at the motel, it must check in at the

front desk and register with Norman Atom. Norman will assign the electron to a bed which is available and as near as possible to the lobby on the ground level. The following procedure will be carried out as long as there are electrons to check in and beds to put them: assignment to the nearest room, one electron to a bed until the room is filled with two electrons to a bed. (Did you remember that every room is equipped with DOUBLE beds?) It should be noted at this point that electrons snore. It is for this reason that when electrons share a double bed, they must sleep at opposite ends (that is, head to foot) so as not to snore and startle the other out of bed. Snoring is repulsive, and electrons are not attracted to each other as it is.

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Arrival:Let’s suppose a Chromium tour bus arrives and allows

Norman to register its electrons.

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7

1s2 [He]

The first electron to check in at the motel will get the first level suite and a double bed all to itself. As the second electron is checked in, it will be assigned to the same room, Suite One, and the other side of the double bed.

8

1s2

2s2

2p6[Ne]

[He]

As a third and then fourth electron register, Norman will assign them to the second level suite since Suite One is filled with two electrons.

As more and more electrons check in, they will be assigned to available rooms as near the ground level as possible. First to the party room on the second level – the first level suite and the second level suite are full. Now, since there are three double beds in Party Room Two, the first electron will get its choice of beds, while the next gets its choice of the two remaining beds, and the third gets the last bed. Please realize that while electrons do not mind sharing, they will occupy an empty bed if it is available.

When the eighth electron checks in, it finds that Suite One is full, Suite Two is full, and Party Room Two has one electron in each bed. It must, therefore, either double up with one of the electrons (sleeping at the opposite end, of course) or expend the extra and unnecessary energy to go to a higher level. It will share; as will the ninth and tenth electrons to check in.

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1s2

2s2

2p6

3s2

3p6

4s2

[Ar]

[Ar]4s2

[Ne]

[He]

As more and more electrons check in, Norman will assign them rooms in the following manner since Level One and Level Two are full: two electrons to Suite Three, then six to Party Room Three (one to a bed and then doubling up, remember). When Suite One, Suite Two, Party Room Two, Suite Three, and Party Room Three are all filled, and option is available: either start occupying the dorm room with its seven double beds or go to the fourth level and use the suite. After all, electrons want to get as close to the ground level lobby as possible and Suite Four is closer than the dorm room on level three.

A similar variance from the expected pattern assignments occurs when Party Room Four fills after Dorm Room Three, Dorm Room Four after Suite Five, etc. This is due to the construction of the motel and the fact that the suites are nearer the ground level lobby, and it takes more energy to go back (and up) to the dorm and faraway rooms. The filling of rooms follows a diagonal pattern.

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1s2

2s2

2p6

3s2

3p6

4s23d4

[Ar]

[Ne]

[He]

[Ar]4s2

Exceptions:There are, of course, exceptions to this order of assignment.

After all, nothing can be this easy and clear cut, now, can it? Once the diagonal pattern has been established, however, the exceptions can seem logical. For example, suppose the fourth level suite has its two electrons but there is an empty bed in the dorm room of level three. Since being in Dorm Room Three takes only slightly more energy and an electron can have a bed to itself, the arrangement of electrons will change to provide two half filled rooms.Stability:

In regard to the exceptions to the rule, the motel management’s (and Norman’s) mental, emotional, fiscal, and physical well-being (stability) is dependent upon how well the available accommodations are filled. It would be ideal to have each room full. If that is not possible, making them half-full is the next best arrangement, or, barring that, putting electrons in pairs so as to keep each other company. This stability will have a lot to do with arrangements of rooms which are on the upper levels and a long way from the lobby.

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1s2

2s2

2p6

3s2

3p6

4s2

[Ar]3d44s2

3d4[Ar]3d54s1

3d5

4s1

[Ar]

[Ne]

[He]

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Diagonal rule

Acknowledgements:As with the dedication of any new edifice, certain persons

must be acknowledged for their efforts in and toward this endeavor: Thanks goes to Max Planck, “you were the one true constant throughout the entire process;” to Neils Bohr, “drop in again anytime you are in this specific area;” to Louis de Broglie, “catch the wave, Louis.”

Thanks should also go to Werner Heisenberg, “where are you Werner? …Werner? …” Oh well, he was here a while ago. To Erwin Schröginer, “since there is no physical meaning for Ψ, Erwin, there’s no point in this thanks;” and to Max Born, “in all probability, you deserve the thanks intended for Erwin.”

However, apologies should go to Alfred Hitchcock, Anthony Perkins, and the cast of the movie whose name was twisted to build this motel: “Sorry for the change Mr., Hitchcock, but the opportunity was there and my mother said I should take a stab at it.”

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Acknowledgements:As with the dedication of any new edifice, certain persons

must be acknowledged for their efforts in and toward this endeavor: Thanks goes to Max Planck, “you were the one true constant throughout the entire process;” to Neils Bohr, “drop in again anytime you are in this specific area;” to Louis de Broglie, “catch the wave, Louis.”

Thanks should also go to Werner Heisenberg, “where are you Werner? …Werner? …” Oh well, he was here a while ago. To Erwin Schröginer, “since there is no physical meaning for Ψ, Erwin, there’s no point in this thanks;” and to Max Born, “in all probability, you deserve the thanks intended for Erwin.”

However, apologies should go to Alfred Hitchcock, Anthony Perkins, and the cast of the movie whose name was twisted to build this motel: “Sorry for the change Mr., Hitchcock, but the opportunity was there and my mother said I should take a stab at it.”

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Ψ-co(The Atoms’ Motel)