As we know, atom is very small. Lets get some idea how small it is.
Let us transform ourself, like Alice in Wonderland, i guess Alice is just 100 times smaller. but this time, we goes much much smaller, become same same as an atom. Hydrogen atom, which is the smallest one, is about 1 meter hight, and Uranium is about 2 meters. and Alice, now becomes mush better then the earth and she can touch the moon easily.
how large is proton in this scale? it is just a diameter of our hair! and electron is still much smaller, so far, we believe that it is just a point, no size. so no matter how powerful your microscope, you never see it! which also means, electron has no internal structure. Thus, you may ask the structure of proton. um… we talk this later.
When someone want to talk about physics, he has to bring up ENERGY. that make his sound professional. and we are going to do the same. However, our unit of energy is different from day usage, like Calorie, or kilo-Watt-hour (kWh). we use MAGA-ELECTRON-VOLT (MeV). before we get some idea about these units. we should understand kilo [k] = 1000, maga [M] = 1000 X 1000.
1 Calorie, which is the energy require the raise 1 degree of 1 kg water. in a cold winter, say 10 degree. if you drink tap water of 350ml, then you lose about 9 Calorie. if you drink 350ml water at 60 degree. then, you gain, 17.5 Calorie. according to this website : If your body mass is 64 kg and you walk at a speed of 5.63 km/hr then you will burn approximately 4.6 Calories/minute – if you walk for one hour you will burn 60 × 4.6 = 276 Calories. well, not much help for the hot water.
1 kWh is equal to 3.6 mage joule. so, what is joule? joule is another energy unit, 1 Calorie = 4.2 kilo joule. Thus, 1 kWh = 860 Calorie = about 3 hour walk. next time when you check your electric bill, you can imagine how far you have to walk to consume this energy.
as you may see, 1 Cal can raise 1 kg water up 1 degree. how many water molecules in 1 kg of water? It is 3 × 1025 !! the world population is just 6 × 109. if this number is money, then every one is a billion billionaire!! So, you can see, each molecule only share very very little among of energy. in order to save some zero in front of 1. we use a very small unit. maga-electron-volt.
according to Einstein Energy-Mass equation: E = m c2, we found that a proton is about 940 MeV/ c2. which is to say, if we want to make a proton out of no where, we have to at least give 940MeV. um, pretty small compare to our daily life. But it is very big in nuclear physics.
from this, we can know electron mass is about 0.5 MeV/ c2.
the reason why we use “energy” unit on “mass”, is not just because Einstein tell us we can do so, but it has a practical reason. We always deal with relativity and using MeV as a unit of mass bring huge convenient, both on calculation and imagination.