A Hydrogen atom has less mass then the combined masses of the proton and the electron that make it up. How can something weigh less then the sum of its parts? Because of “E=mc²”
E=mc² is probably the most famous equation in all of physics. However, what does it really mean? Most surprisingly, in the original 1905 paper, Einstein actually wrote it down as m=E/c². That’s because in the core of it, there is a lesson in how to think about mass.
I have personally used statements like “Mass is frozen Energy”, or “Mass can be converted to energy” to find out, after doing this research, none of them is correct.
What Einstein really wants us to know is that mass is not anything at all. It sounds a bit confusing, however, with these examples we will understand it hopefully.
Let’s take to watches that are identical atom from atom.
except that one of them is fully running and ticking, and the other one has stopped. According to Albert Einstein, the ticking watch has greater mass then the one that has stopped. The question is, why? Well, in Einstein’s theory (which is correct), the hand and gear are moving, so they have some kinetic energy. There are also some wound up springs in the running watch that have potential energy, and there is a little bit of a friction between the moving parts and the watch, therefore the parts get heated up that the atoms start jiggling a little bit, that is thermal energy. Now what m=E/c² says is that all of that kinetic and potential and thermal energies that reside in the watch’s parts manifest themselves as part of the watch’s total mass. How does it happen? Simple, You just add up all of those energies (kinetic, potential, thermal) divide them by the speed of light squared, and that is how much extra mass that those energies contribute to the hole. Since the speed of light squared is too huge which is equal to “8.98755179 × 1016 m² / s²” the extra mass is too tiny, only about 0.000000000000000001% or 1e-20. This is why, according to Einstein most of us have that mass is an indicator of amount of matter in an object, simply, IT IS NOT! It’s just in everyday life we do not notice, because it is too small, but not zero though.
The next example is easy:
When you turn on your flashlight, its mass starts to drop immediately. The light carries energy, this energy was previously stored electrochemical energy inside the battery, and therefore manifesting as part of the flashlight’s total mass.Since the energy escaped we are not weighing any more. All of that happens because of m=E/c². Same Applies to the sun.
So the sun’s mass will drop. Isn’t that bad? Well, no. Even though it’s mass drops just by virtue of the fact that is shines, by about 4 billion kg every second (4,000,000,000 kg/s), that’s just 1/1021 of the sun’s mass, and only 0.07% of the sun’s mass over it’s entire 10 billion year life span.
Even this doesn’t mean that the sun converts mass into energy. All the energy in the sun light came from other energies, kinetic and potential energies of the particles that make up the sun. Before that light was emitted, there was simply more kinetic and potential energies of its contained within the volume of the sun, manifesting as part of the sun’s mass. Those 4 billion kg that the sun loses every second are simply just a reduction in the kinetic and potential energies of its constituent particles. What we have been weighing is the energies of the particles in objects all along we just did not notice.
Do you remember the first sentence,”A Hydrogen atom has less mass then the combined masses of the proton and the electron that make it up.” Well how can that happen?
It is because potential energy can be negative. We say that the potential energy of a proton and electron when they are infinitely far apart. Since they attract each other their electric potential energy will drop when they get closer together, like your gravitational potential energy drops when you get near the surface of Earth, which is also attracting you. So the electric potential energy in the hydrogen atom is negative. But the the electron in the hydrogen atom also has kinetic energy, which is always positive, due to its movement around the proton. However, it turns out that the potential energy is negative enough that the sum of the the kinetic and potential energies is negative. Therefore, m=E/c². In-fact, all of the elements in the periodic table weigh less than he sum of their parts that make them up. Same applies for molecules. Lets take the oxygen molecule, it weighs less than the two oxygen atoms that make it up.
Thanks for reading.
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