10.8: Quantum Mechanics
- Page ID
- 476565
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- Properly explain the possible locations of electrons within an atom based on quantum mechanics.
How do you study something that seemingly makes no sense?
We discuss electrons being in orbits, and it sounds like we can tell where an electron is at any moment. We can draw pictures of electrons in orbit, but the reality is that we just do not know exactly where they are. We will take a quick look at an area of science that even leaves scientists puzzled. When asked about quantum mechanics, Niels Bohr (who proposed the Bohr model of the atom) said, "Anyone who is not shocked by quantum theory has not understood it." Richard Feynman (one of the founders of modern quantum theory) stated, "I think I can safely say that nobody understands quantum theory." So, let's take a short trip into a land that challenges our everyday world...
Quantum Mechanics
Earlier in this text we discussed classical mechanics, the study of the motion of macroscopic objects like people and balls and vehicles. Because of the quantum nature of the electron and other tiny particles moving at high speeds, classical mechanics is inadequate to accurately describe their motion. Quantum mechanics is the study of the motion of objects that are atomic or subatomic in size and thus demonstrate wave-particle duality. In classical mechanics, the size and mass of the objects involved effectively obscures any quantum effects, so that such objects appear to gain or lose energies in any amounts. Particles whose motion is described by quantum mechanics gain or lose energy in the small pieces called quanta.
One of the fundamental (and hardest to understand) principles of quantum mechanics is that the electron is both a particle and a wave. In the everyday macroscopic world of things we can see, something cannot be both. But this duality can exist in the quantum world of the submicroscopic on the atomic scale. There are even more baffling aspects of quantum mechanics we could explore, but we will focus on developing a model that we can use to make some sense of what is going on with these electrons.
One of the tenants of quantum mechanics is that any moving object also has wave properties. (The specific relationship is called the de Broglie wave equation, but we will not explore it in detail.) The wavelength is inversely proportional to the momentum of the moving object. It turns out that for a large object, this wavelength ends up being so small as to be essentially meaningless. On the other hand, particles with measurable wavelengths are all very small. However, the wave nature of the electron proved to be a key development in a new understanding of the nature of the electron. An electron that is confined to a particular space around the nucleus of an atom can only move around that atom in such a way that its electron wave "fits" the size of the atom correctly. This means that the frequencies of electron waves are quantized. Based on the equation \[E=hf \nonumber \] the quantized frequencies mean that electrons can only exist in an atom at specific energies, as Bohr had previously theorized.
Energy Levels and Electron Orbitals
Energy levels (also called electron shells) are fixed distances from the nucleus of an atom where electrons may be found. You can stand on one step or another but not in between the steps. The same goes for electrons. They can occupy one energy level or another but not the space between energy levels. This sounds very much like the Bohr model of the atom we introduced previously, but there are a few key differences that we will note.
The model in Figure \(\PageIndex{2}\) shows the first four energy levels of an atom. Electrons in energy level I (also called energy level K) have the least amount of energy. As you go farther from the nucleus, electrons at higher levels have more energy, and can hold more electrons. The difference between this model and the Bohr model is that we are not specifying the location or direction of movement of the electron, simply the potential energy of the electron based on its distance from the nucleus.
You might wonder what the movement of the electron looks like if it is not circling the nucleus like a planet circles the Sun. The mathematical model for the behavior of electrons resulted in what are referred to as wave functions. These only indicate the probability of where the electron is most likely to be found (and conversely, were it might not be allowed to exist.)
The location of the electrons in the quantum mechanical model of the atom is often referred to as an electron cloud. The electron cloud can be thought of in the following way: Imagine placing a square piece of paper on the floor with a dot in the circle representing the nucleus. Now take a marker and drop it onto the paper repeatedly, making small marks at each point the marker hits. If you drop the marker many, many times, the overall pattern of dots will be roughly circular. If you aim toward the center reasonably well, there will be more dots near the nucleus and progressively fewer dots as you move away from it. Each dot represents a location where the electron could be at any given moment. Because of the uncertainty principle, there is no way to know exactly where the electron is. An electron cloud has variable densities: a high density where the electron is most likely to be and a low density where the electron is least likely to be, as shown in Figure \(\PageIndex{3}\).
In order to specifically define the shape of the cloud, it is customary to refer to the area within which there is a \(90%\) chance of finding the electron. This is called an orbital, the three-dimensional region of space that indicates where there is a high probability of finding an electron. Figure \(\PageIndex{4}\) shows some models of electron orbitals. Note that not each of the possible orbitals results in a spherical shape.
Section Summary
- Quantum mechanics involves the study of material at the atomic level where the particles motion is described by gaining or losing the discrete amounts called quanta.
- In quantum mechanics, electrons exist simultaneously as both a particle and wave.
- This field deals with probabilities since we cannot definitely locate a particle.
- Energy levels (also called electron shells) are fixed distances from the nucleus of an atom where electrons may be found. As you go farther from the nucleus, electrons at higher energy levels have more energy.
- The location of the electron can only be given as a probability that the electron is somewhere in a certain area.
Glossary
- quantum mechanics
- study of the motion of objects that are atomic or subatomic in size and thus demonstrate wave-particle duality
- quantized
- something that only has certain values allowed
- energy levels
- fixed distances from the nucleus of an atom where electrons may be found
- wave functions
- mathematical model for the behavior of electrons which indicates the probability of where the electron is most likely to be found
- electron cloud
- an indication of the most likely locations of the electron in the quantum mechanical model of the atom
- orbital
- three-dimensional region of space that indicates where there is a high probability of finding an electron