You are a teacher or a student in chemistry; you are talking to a student or a friend about Quantum Mechanics, trying to explain to him/her the concept of quantization of energy /orbits and orbitals.
Question:
What example(s) or analogy in real life can you use to help to better understand the following concepts?
- Quantization of energy vs Ordinary forms of energy?
- Atomic orbitals?
Solution:
(The following are not the only examples/analogies that answer Question 7, many others can be found; it’s up to your imagination!)
1. Quantization of energy vs Ordinary forms of energy?
- The image below represents a ramp. When you walk on a ramp, any pace is allowed: 1m, ¾ m, ½ m, etc. In other words, this system allows any amount of energy or any length of your pace. This is what happens in almost daily situations and is dealt with in Classical Mechanics.
Photo by Jon Tyson on Unsplash
- Quantization of energy: one of the concept introduced by Bohr’s atomic model is that electrons move around the nucleus in discreet, allowed or quantized energy levels. In other words, some amounts or levels of energy are allowed, others are not. But only if the electron receives/absorbs the appropriate amount of energy, it can then jump to a higher energy level, and it is said to be excited. If it loses the absorbed energy, it falls back to the level where it was before and it is said to be de-excited. This explains the source and existence of atomic spectra, absorption spectrum and emission spectrum of an atom.
To help understanding that concept, we can compare quantized energy levels to a staircase. When you walk on a staircase, you only put your feet on different steps, not between the steps. The different steps of the staircase can be compared to the allowed energy levels. You cannot step between the steps, those positions are not allowed. You can walk only on the staircase step by step, you can also jump the steps to fall on an allowed step (image below). Therefore your moving up or down a staircase is quantized.
Photo by Ellen Auer on Unsplash
You can also use the example of a lift or an elevator in a building: a lift or an elevator will pick and drop people at different floors or levels of the building, never between the floors or levels: the moving of the elevator up and down the building is a quantized movement. Only some positions (floors) are allowed.
You can also use the example of a shelf (bookshelf or any other kind of shelf). When you put an object on a shelf, you put it on a given shelf where a place is available; you cannot put it between the shelves; because the place between the shelves is not allowed and only shelves are allowed. You can move that object, a book for example, from one shelf to another, above or below, if there is an empty place on that shelf. And when a shelf is full, you cannot put any more objects (more books for example) on that shelf. This resembles to what happen with electrons on different atomic energy levels and orbitals.
Another example; you are in a Grocery store and you decide to buy fruits (Oranges, Apples, Passion Fruits, etc.). You have no choice than to buy 1 fruit or a whole number multiple (x2, 3, 4, 5) of that fruit; you cannot buy a fractional number multiple, example 1/2, 2.5, 3.25, of the fruit. This represents also a kind of a quantized phenomenon. Compare the oranges to packets of energy or quanta of energy, also called photons, and one orange to one packet of energy or one quantum of energy, also called one Photon and represented by the relation:
E = hγ,
where E = energy of the photon, h = Planck constant = 6.626 x 10-34Js, γ = frequency of the light (photon).
2. Atomic orbitals
For the orbital, we can compare it to the compound of a boarding school, and electrons to the boarding students. During the schooling period, the parents of a boarding student can say, with high probability that the boy/girl is in the school compound; but they cannot precise which point of the compound he/she is at.
Another condition is that the boarding student cannot leave the school compound, unless he/she gets permission to go out for a limited time and come back. This is to be compared to the excitation energy given to an electron to allow it to jump from one orbital to another of higher energy.
In all of this, absorption of energy in form of light that results in an excited state explains the origin and existence of atomic absorption spectra. But as the excited state is unstable and short-lived, the excited electron loses the absorbed energy in form of light to return to its non-excited state called ground state; this explains the origin and existence of atomic emission spectra.
(You can revisit Problem 5: IV. Bohr’s atomic model, absorption and emission spectra as well as emission flames)