Figure 2. The German physicist Max Planck had a major influence on the early development of quantum mechanics, being the first to recognize that energy is sometimes quantized. Planck also made important contributions to special relativity and classical physics. Using the quantization of oscillators, Planck was able to correctly describe the experimentally known shape of the blackbody spectrum.
This was the first indication that energy is sometimes quantized on a small scale and earned him the Nobel Prize in Physics in It was such a revolutionary departure from classical physics that Planck himself was reluctant to accept his own idea that energy states are not continuous. Planck was fully involved in the development of both early quantum mechanics and relativity.
This 0. But on a macroscopic or classical scale, energies are typically on the order of joules. Even if macroscopic energies are quantized, the quantum steps are too small to be noticed. This is an example of the correspondence principle. For a large object, quantum mechanics produces results indistinguishable from those of classical physics.
Now let us turn our attention to the emission and absorption of EM radiation by gases. The Sun is the most common example of a body containing gases emitting an EM spectrum that includes visible light. We also see examples in neon signs and candle flames. Studies of emissions of hot gases began more than two centuries ago, and it was soon recognized that these emission spectra contained huge amounts of information.
The type of gas and its temperature, for example, could be determined. We now know that these EM emissions come from electrons transitioning between energy levels in individual atoms and molecules; thus, they are called atomic spectra.
Atomic spectra remain an important analytical tool today. This constant regulates and "quantizes" the energy of the universe. What is quantization of energy? Physics Atomic Physics Quantization of Energy. Oct 19, Related questions Why are quantum numbers like an address? How many quantum numbers are used to describe an electron? It turns out the electrons follow a simple principle, namely, they go into the lowest energy shell that is available.
If a lower energy shell is full, they go into the next lowest energy shell. A crude analogy is putting water into a pail; the water always fills from the bottom!
Look at Figure 5 again, which represents an atom with 13 electrons. Notice how the lower energy shells are full, and the last three electrons go into shell 3, which is not full. Additional electrons would continue to go into shell 3 until it is full with 8 electrons, for a total of A 19th electron would be forced to go into shell 4. Since it is not specified that the atom is charged, we presume it is neutral.
Aluminum has 13 protons, so neutral aluminum would have 13 electrons. Put 2 electrons in shell 1 which fills it, next put 8 electrons in shell 2 which fills it, and the last three electrons go into shell 3.
Look at the number of elements in each row of the periodic table. Rows 1 through 4 contain 2, 8, 8, and 18 elements respectively. Now look at Table 1. Is this a coincidence? In fact this shows that the patterns of elemental properties that the periodic table reflects have their basis in electron configurations. Consider Figure 6 which shows the electron shell models of hydrogen, lithium, sodium, and potassium.
See how each has one electron in its highest energy shell. Now find these elements on the periodic table. They are all in the first column of the periodic table. Consider the elements of the last column of the periodic table draw them out for yourself. They all have full outer shells.
A general relationship begins to emerge: elements in the same column on the periodic table have similar electron configurations. Originally, the periodic table was constructed based on observable chemical and physical properties. Elements that behaved similarly were placed in the same column; however the chemists had no explanation of why they were similar.
Now with the electron shell model we have a theory that helps us understand the reasons for these similarities. Likewise, if a particle goes to a lower energy level, that energy must be transferred into another system. We know that energy is conserved if we consider all systems involved in the process of energy transfer.
So what systems gain or lose energy to our particles? The most common systems that accept and give energy to systems of small particles are electromagnetic waves light and the vibrations of molecules heat or sound.
We will talk about the energy of light in more detail below. The collection of allowed energies a system may have is called the energy spectrum of that system. The levels in the spectrum tell us the total energy the particle is allowed. Typically, the total energy is the sum of the kinetic and potential energies. The energies that a system is allowed to have depend on the potential energy of the system.
Each unique container has its own set of energy levels. As discussed earlier in this volume and in previous quarters, the exact potential energy of a particle is not important, but the changes in potential energy really matter.
In quantum mechanics, this is still the case. In effect, we can set "zero" potential energy to be at any level, so in our examples we will establish conventions that make interpreting the results as simple as possible. In the example mentioned in the text where the particle can have 1 J, 4 J, 9 J, or 16 J of energy, what is the energy spectrum? What is an example of an energy level? Just as we can think of ordinary matter being quantized as illustrated by the example with water , we also find that light comes in indivisible quanta that we refer to as photons.
Unlike atoms, we do not model these photons as being made up of smaller particles. We will discuss photons in more detail later, but at the moment we establish two facts about photons:. A useful analogy to different types of light is different elements. To a good approximation we can imagine that mass is quantized; the quantum of mass is the mass of individual atoms after all, it is hard to break apart atoms!
However the atoms of different elements have different masses. Similarly, each photon is an indivisible quantum of light, but photons of different frequencies contain different amounts of energy.
So the smallest amount of energy in light is different for each type of light. Gaining a better understanding of three important energy spectra will help us learn about a large variety of phenomena.
The first spectrum we will consider is that of the infinite potential well. In this system, a particle is trapped between two points in one dimension, and can't escape no matter how much energy it has. We contrast this with a harmonic oscillator like a mass on a spring , where the width of the "well" depends on how much energy the particle has. The third system we will explore is the system of an electron bound to a nucleus a hydrogen atom. Energy spectrum examples for each of these three systems are shown below respectively, left to right.
By convention, the vertical axis represents energy; the horizontal has no meaning. When looking at these spectra, notice how the spacing between consecutive energy levels is different in the three situations.
The levels are evenly spaced for the oscillator center , closer together at low energies for the infinite well left and closer together at higher energies for the hydrogen atom right. The infinite potential well is a system where a particle is trapped in a one-dimensional box of fixed size, but is completely free within the box.
To keep the particle trapped in the same region regardless of the amount of energy it has, we require that the potential energy is infinite outside this region hence the name "infinite potential well".
We then set "zero" potential energy to be the energy inside the box. The infinite well seems to be the least useful of the situations we will study; very few physical situations are similar to the infinite well. We introduce this system because it has the simplest potential available. If a particle is inside the box then it has no potential energy.
If the particle is anywhere else, it has infinite potential energy. Because our particles can only have finite energy this ensure the particle stays in the box. Also, since there is zero potential energy inside the box, the total energy of the particle is equivalent to the kinetic energy of the particle. If the particle gains total energy, we know it must have gained kinetic energy.
We derive the equation for a trapped particle later, but for now, we will make sense of the equation without worrying about its derivation. The potential energy is zero inside the box, so the particle always has some kinetic energy. For a quantum particle in a box it is impossible to sit at rest. Suppose you have a particle in the ground state of the infinite square well potential.
You also have a device allowing you to add energy to the particle. You try to add an infinitesimally small amount of energy, but nothing happens, because only certain amounts of energy can be gained by the particle. What is the smallest amount of energy you can successfully transfer? This means the gaps between lower energy levels are smaller than those between higher energy levels.
So as the particle gains energy, it takes more energy to transition to a higher level. So if the potential well becomes wider, it becomes easier to transition between levels. The protons and neutrons of an atom are confined to the nucleus. Give an estimate of how much energy we would need to move a proton in Helium up to the next energy level. We guessed! This answer is only a rough estimate, but it gives us some idea of the amount of energy involved.
To make a meaningful comparison, the amount of energy it takes to break a chemical bond has a typical magnitude of 1 eV. The next potential we consider is the harmonic oscillator.
A microscopic particle that is constrained by a spring-like potential for instance, the atomic bond potential will also have quantized energy levels. For this potential, the energy levels are equally spaced, and the spacing is related to the frequency of the oscillation.
The potential energy between bonded atoms is similar to the potential energy for mass-spring systems — atoms oscillate even at 0 K! This energy cannot transfer from the mass-spring to another system because there are no lower energy levels available to the mass-spring system.
A friend of yours points out that a mass-spring in the lab would also have quantized energies due to this formula. Because the energy depends on amplitude, this would mean that you are only allowed certain amplitudes. Yet in the lab, it seems that you can set the amplitude to an value you want. How do you resolve this discrepancy?
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