December 16th 2016
In our previous post (which you should read if you haven't already) we discussed the conundrum that early twentieth century physics observed. They discovered that our world is made up of atoms that consist of a positively charged nucleus and negatively charged electrons but that they are almost entirely empty space. Treating the system using classical physics equations led to really strange results that didn’t line up with reality- why does the electron exist in a region away from the nucleus instead of simply spiraling inward? Wouldn’t Coulomb attraction predict that opposite charges should just attract until they are touching?
Around this time that the stability of matter was being investigated after the discovery of the nucleus and the electron, other research using hydrogen gas shed light on this problem. If a high voltage is applied to a glass tube that is filled with hydrogen, the gas will glow. Surprisingly, only specific colors are observed to emanate from the tube. (Think about how each tube in a neon sign is only a single color, hydrogen has this behavior as well.) Niels Bohr stated that the reason why we only see certain colors of light coming from the glowing hydrogen is due to how the atom is arranged.
Instead of the electron being able to occupy an arbitrary distance from the nucleus, the electrons must occupy specific states that have different radii. An electron in a lower state (left) can be excited by the high voltage source into a higher energy state (middle). At a later time, the electron will relax back to its normal (so called ground) state. Since energy can’t be created or destroyed, that energy given to it by the high voltage source has to go somewhere and it is released as a single photon, or light wave.
The energetic states are characteristic of the atom itself and so hydrogen on earth will have the same energy spacing and glowing pattern as hydrogen on on the Sun, for example. What’s important is that there are only a certain allowed states and that the electron cannot occupy arbitrary distances in between. We say that the electrons are quantized because they are confined to this finite number of possible positions. This observation doesn’t actually tell us why we never observe electrons in the nucleus, but it does suggest that it doesn’t occur.
One of the most important factors that prevents the electrons from collapsing into the nucleus is a quantum mechanical concept of uncertainty. It says that we cannot have complete information about the state of our system, in particular we cannot know its position and momentum with complete certainty.
This type of uncertainty is different from uncertainty in our day-to-day lives. For example, I can be uncertain about where in downtown Chicago I may be but if I pull out my GPS, I can determine it immediately. Electrons, however, do not have the properties of a definite position or momentum, instead these properties are described by a probability distribution, which just means that there is a spread of possible positions and momentums that the particle has at the same time (See example below).
Since electrons do not have a well defined position, the more we try and confine the electron’s position, the more uncertain its momentum would be and vice versa. If we knew that the electron was confined to the nucleus, the high degree of spatial precision would lead to an uncertainty in momentum that would be so high that the electron would at some point have sufficient momentum to break free from the atom itself.
Another way to think about the uncertainty is by calculating the electron’s wavelength to see how that compares to the radius of the nucleus. Objects with shorter wavelengths will be more localized while longer wavelengths are less localized but their momentum is better defined. The wavelength of an object is dictated by its mass and this formula:
λ = h / m c
Here, h is plank’s constant and c is the speed of light, so the wavelength is only dependent on the mass. We can calculate the wavelength of an electron to be 386 fm. The size of a nucleus is 1 fm which is more than 300 times smaller than the wavelength. This means that if we would like to confine the electron’s wavelength to be 300 times smaller, the mass of the electron would need to be 300 times heavier which is not observed. Thus, in a sense the electron is too lightweight to be confined to the nucleus.
Layout of a Helium Atom
Part of the reason why electrons occupy stable electron clouds around the nucleus is due to the four fundamental forces in nature and the differences in their relative strengths. Protons and neutrons both are made up of even smaller species called quarks, which are governed by the ‘strong’ nuclear force. This force is ~100 times stronger than the ‘electromagnetic’ force that causes the attraction between a positively charged proton and a negatively charged electron.
This difference in attraction between the strong and electromagnetic force means that the protons and neutrons attract each other ~100 times more strongly than electrons and protons do. Even if you were able to create configurations of protons and electrons in some sort of neutral lattice, the lack of a ‘strong’ nuclear force between the two species means that the slightest knock would cause the whole species to blow apart.
An exciting part about science is that experiments only tell us facts and it is up to us to figure out an interpretation of how the facts all fit together. Experiments allow us to collect new facts which sometimes don’t fit with previously held theories, but if we are clever we can come up with better theories that better encompass all of the facts.
In this post I gave several explanations for why electrons don’t fall into the nucleus but instead form a diffuse electron cloud. First, we can verify with experiments that electrons always occupy specific positions from the nucleus. Uncertainty in quantum mechanics tells us that an electron localized to a nucleus is much more unstable than when the localization is broader and that in order for an electron to be sufficiently confined, it would have to be significantly heavier than we observe. We also learned that the strong nuclear force is 100 times stronger than the electromagnetic force which explains why protons attract neutrons much more strongly than neutrons.
Now that we know why atoms don’t collapse in on themselves, we still need to discuss how electrons interact and repel other electrons, which keeps us from falling to the center of the Earth. Our next post will cover that topic and how it leads to chemical bonding. Stay tuned!
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