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This mass number is equivalent to the actual mass of the nucleus but not quite the same. The actual mass of the nucleus is measured in the unit u which stands for “unified atomic mass unit” and is defined as “1/12th of the mass of a carbon nucleus with 6 neutrons” *. In the English speaking world, this u is often replaced with the Da, the Dalton, named after John Dalton. The unit u is also the unit you used in the exercises in the chapter about Berzelius.
How does this help us?
The unit u because useful when you know the amount of particles. The amount of particles is given in the amount of moles. A mole is (apart from the small burrowing creature) a specific amount. One mole is 6,02214076.1023 particles. The unit u and Da have been chose so that when you have a particle that weighs 26,9815386 u, 1 mole of that particle weighs exactly 26,9815386 grams.
This fact is of huge importance in chemistry. In a reaction scheme, you can see how many molecules of substance A react with how many molecules of substance B. Because one mole is always the same amount of particles, that ratio of molecules is also the ratio between moles of those molecules. By using the relative atomic mass measured in u, you can calculate the amount of grams each mole of molecules is and with that, how many grams of substance A reacts with how many grams of substance B.
Thanks to the unit u, you can calculate the amount of grams you need to weigh out, the unit u is the connection between the reaction scheme and the experiment!
When do things become weird.
Because carbon has atomic number 6 and therefore has 6 protons, you might conclude that every proton and neutron has a mass of 1 u but sadly, reality is not that kind. The mass of a proton (at rest) is 1,007276466812 u and the mass of a neutron is 1,00866491600 u. This of course begs the question “If every proton and every neutron has a mass over 1 u, how can a nucleus with 6 protons and 6 neutrons have a mass of just 12 u?”.
This is because the mass of a subatomic particle changes when it is bound inside of a nucleus. The mass that is “lost” is converted into energy using E=mc2 and lost to the environment. This energy is called the binding energy and it is this amount of energy that you need to take the atom apart again. You’ll see this energy again in chemistry.
*In 2019, the kilogram was redefined. Before, the kilogram was defined as the mass of a platinum-iridium cylinder kept in Paris but now, its definition relies on constants of nature. During this redefinition, it was also necessary to redefine Avogadro's number, the amount of particles in a mole and with it, the mass of u. So the u is no longer exactly 1/12th of the mass of a carbon-12 nucleus but the difference is minute.
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