I have done a poor job in keeping current with these posts. So, to bring this back, what better topic than to continue with random physics discussions.
Let’s look at Einstein’s famous equation… E = mc2.
E, energy, which stands on its own side of the equation.
m, mass, which relates to energy by a conversion factor.
c^2, the speed of light squared, or the conversion factor to make mass and energy equivalent (i.e., linking mass and energy).
For hundreds of years, energy and mass evolved as separate systems under prevailing conventional physics understanding. They developed independently. Physicists did not believe that energy and mass could be linked into a common system. However, Einstein helped show that energy and mass can be linked.
But, in order to link two independent systems, you need a conversion factor. When converting from Celsius to Fahrenheit, the conversion factor is multiplying by (9/5) and adding 32. When converting from inches to centimeters, multiply by 2.54. In each example, these are conversion factors for linking the two systems (Celsius / Fahrenheit and inches / centimeters).
In the case of energy and mass, the speed of light is the conversion factor. Specifically, the speed of light squared.
Picture a space shuttle chasing after a light beam. It’s trying to catch up to the speed of light (186,000 miles per second). Imagine the space shuttle is just shy of the speed of light. As the pilot further hits the throttle to chase after c, since he can’t reach it, that incremental energy swells into mass. The space shuttle gets larger and larger. Why?
Because energy cannot leave the system, and if c is maxed out (nothing can go above the speed of light - it’s the upper limit), then the energy must translate into mass. Scientists have observed this mass swelling phenomenon when speeding up photons.
This is a fundamental thought experiment of Einstein’s - imagine yourself chasing after a light beam.
His equation dictates that one can never truly catch up to a light beam - it will always be slightly ahead.
As an object with mass accelerates and approaches the speed of light, its relativistic mass increases, and the amount of energy required to continue accelerating also increases. As the rocket ship gets closer and closer to the speed of light, the incremental energy required to accelerate it further approaches infinity.
There is another explanation for why objects with mass cannot travel at the speed of light, and it deals with spacetime geometry. However, since it doesn’t directly apply to the equation which is the topic of today’s post, we’ll come back to this second explanation later.
E = mc2
Moving back to the equation, visualize the “=” in the equation as a tunnel or bridge. As very little mass gets sent across the tunnel, it gets enormously magnified on the side of energy. The reason is because of the large conversion factor (i.e., the large figure of the speed of light).
Mass is simply the ultimate type of condensed or concentrated energy. And you can turn mass into energy, so the conservation of mass does not need to hold. What does hold is that the total quantity of energy and mass remain the same despite converting mass to energy or vice versa. The system of our universe cannot lose the sum of energy and mass.
Radioactivity
Marie Curie, a pioneering physicists and chemist, dubbed the term radioactivity in 1898. She introduced the term as she was studying radiation by certain substances. These substances, or metals, achieved their power by sucking immeasurably tiny portions of their mass out of existence. Then, they would switch that mass into the greatly magnified form of energy.
The source of energy is converting the substance’s own mass and sending it across the tunnel, and, as we know, becoming immensely magnified when multiplied by c2.
One fascinating part of Einstein’s equation is that it implies that any substance can have its mass exploded outwards as energy.
As we will explore, the equation is how an atomic bomb, with a core that could fit in your hand, has the power to decimate an entire city.
Nuclear Model of the Atom
In 1910, Ernest Rutherford developed a better understanding of what’s inside an atom… mostly empty space! Electrons float on the outer walls of the atom and are negatively charged particles. Protons are found in the dense nucleus and are positively charged. Neutrons, as the name infers, are electrically neutral particles.
To picture this vast space in an atom, imagine a meteor hurtling towards Earth and diving into the ocean. Rather than eventually stopping upon hitting the ocean floor, the meteor continues and pops out the other side of the ocean. That’s the way to think about the space of an atom. The caveat being that within this vast ocean exists a small, dense nucleus.
Niels Bohr had a model for how to think about a nucleus. Rather than view it as a rigid metal, like a collection of ball bearings welded tightly together, think of the nucleus as a liquid drop.
A water drop is always on the verge of bursting apart… due to the weight inside of it. For a nucleus, the bursting weight is represented by the crackling electric charges between the protons. All of the protons push against each other (as they are all positively charged and thus repel).
But, the water drop stays together because of the rubbery surface tension on the outer surface. This surface tension is the glue-like fabric and strong force that holds the protons together within the nucleus.
In a small nucleus, such as that of carbon for instance, the surface tension force is so strong that it doesn’t matter that there is lots of electric power hidden away inside, trying to push the protons apart.
But, in a big nucleus, especially a very large one like that of uranium, could injecting extra neutrons trip the balance?
Neutrons and the Nucleus
In the 1930s, physicists discovered that you could send slow moving neutrons into the nucleus. The neutron is capable of penetrating the positively charged nucleus (remember how the nucleus is filled with protons) because it is electrically neutral and thus won’t be repelled by electric forces.
This is a groundbreaking discovery for we will see what follows next.
Back to uranium. By adding neutrons to the uranium nucleus, you can split the nucleus and form two nuclei.
Even more interestingly, the division of a nucleus in two results in two uranium nuclei that would be lighter than the original uranium nucleus.
Put differently, in splitting a nucleus, you lose mass… which means that you create energy.
We know from Einstein’s equation, E= mc2, that when mass disappears, energy is created.
How much energy / how much lighter is the nucleus? About 1/5 the mass of a proton or 200 million electron volts (200 MeV - the units being mega-electron volts). For context, there was a Berkley magnet that when charged with more electricity than the whole city would ordinarily use in one day, would power up a particle to 100 MeV of energy.
This is the power of c2 - that a tiny amount of mass can produce an enormous amount of energy. c2 is the widening bridge that connects the world of energy to the world of mass.
Splitting an Atom
One day in the late 1930s, two physicists were walking along a snowy path in the mountains. They came to a monumental conclusion - that everyone had been wrong about how to split the atom.
Conventional wisdom suggested that you had to blast neutrons harder and harder at the nucleus.
However, what these physicists concluded, is that you don’t have to supply the power for a uranium atom to explode. Just get enough extra neutrons in there to start off the reaction and then the dominos will fall. A chain reaction will follow.
By sending in the first neutrons, the already stretched nucleus will begin to jiggle… it will jiggle more and more until the strong forces that hold it give way… and the forces of the protons inside make the fragments fly apart.
The explosion essentially powers itself, with the help of a source spark (the initial neutrons).
These scientists dubbed this process / discovery as fission. In Latin, fissio means “a splitting.” The physicists pulled the term from the behavior of bacteria in how those cells divide rapidly to increase their population.
The Equation’s Chain Reaction
30 years after Einstein introduced E = mc2 in his famous 1905 paper, physicists had shown that the atom could be opened. Not only that, but the compressed energy inside a nucleus could be harnessed and let out (by channeling mass through the tunnel of the equation’s “=” and multiplied by c2).
They found the nucleus and discovered the particle that could traverse in and out of the nucleus (a neutron), especially when sending the neutron slowly.
And, importantly, they found that when extra neutrons are pushed into an overstuffed atom such as uranium, the whole nucleus wobbles, trembles, and then explodes…
As previously mentioned, as the weight of the nuclei after this process is lower than the weight of the original nucleus, that is what leads to the intense energy creation that powers this high-velocity escape.
As all of this was on the front edge of discovery, the world entered into its largest war ever.
Now began the race to see who could harness the power of Einstein’s equation.
Conclusion
To summarize, in these 30 years, physicists discovered that you can send slow moving neutrons into a nucleus. Fast moving neutrons are too “streamlined” as they travel and are less likely to be caught by the nucleus. Slow moving neutrons tend to wobble more and are therefore more likely to catch on to a nucleus and get pulled in.
Once the neutron is pulled into the nucleus, E=mc2 can take hold —> the nucleus wobbles, then explodes, letting out its great blasts of energy, and also letting out a gush of extra neutrons, which then hit more nuclei, pushing them to wobble and explode apart in turn.. that’s the chain reaction.
An interesting side note is how to slow neutrons. In the early 1930s, in the first experiments on this topic, physicists discovered that using water partially slows neutrons. However, when Heisenberg (the lead physicist for Nazi Germany) began building Germany’s bomb, he needed something that would slow neutrons more than water could.
The reason that water partially slowed the neutrons is because hydrogen slows these particles, and water is partially composed of hydrogen (H2O).
However, Heisenberg then discovered that he could use “heavy water” as his neutron moderator to slow down the speed. Heavy water (D2O) is composed of deuterium, which is a hydrogen isotope that has one proton and one neutron. Hydrogen, the most common isotope being protium, has one proton and no neutrons. The additional neutron in deuterium is very effective in slowing down the neutrons when sending to a nucleus.
So, Heisenberg quickly advanced Germany’s ability to develop the bomb through his usage of heavy water, in addition to Germany’s access to large quantities or uranium.
In the next post, we can dive into interesting developments around Heisenberg’s bomb program and Britain’s attempt to deter these efforts.
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Until next time.
John Galt