 Hi. I'm Zor. Welcome to Unisor Education. We continue talking about units of measurements and today we will talk about how we measure mass of objects. Well, we have already spoken about seconds as the unit of time and meters as the unit of lengths. Now, it's been a decision actually of physicists to use the units of measurements based on certain natural physical constants which do not really depend, the value of which does not depend on whatever we are doing. So it's not supposed to be something artificial, it's supposed to be based on something objective. And that's why we have defined second the unit of time. That was the first unit which needed to be defined as the time for certain atom of cesium to make oscillations in certain number. Number was 9192 631 770. So the atom of cesium, if it transforms from one state to another and the states are supposed to be defined properly, we are not talking about what kind of states, but it's like agitated state and normal ground state. So number of these oscillations is exactly the time which is equal to one second. So we have defined the second and similarly we have defined the unit of measurement as being the distance covered by light in vacuum during 299, was 72458 of a second. So second is already defined. That's the time which takes the atom of cesium to make these many oscillations. And now since second is defined, this piece of a second needed for the light in vacuum to cover the distance in one meter. So meter is also defined. Now the logic is to always define the next unit of measurement in terms of some physical constant and already defined previously defined units. So we have a very strict hierarchical kind of construction. So we defined something like a second based only on some phenomenon. Then we have defined it lengths based on some phenomenon and already defined second. And now we will define the unit of mass which is called kilogram based on already defined units, time and lengths and some physical constant. So again, that's the general direction. Okay, now let's talk about how it was actually defined. Well, in 1889 actually they have decided to make a standard kilogram. Now before that the unit called gram existed and that was basically the mass of one cubicle centimeter of water. By the way, centimeter is already defined now at least. But the problem is, I mean, you can't really have a precise measure based on cubicle centimeter of water. Well, it depends on the water, temperature, et cetera, et cetera. It's not really constant. In 1889 they have decided to make an object, a real object which has a mass of one kilogram and they did it. Remember how they did the unit of measurement, the meter as a metal rod somewhere in the 19th century and put it in some laboratory? Well, later on they have decided to get all this particular standard because it's not precise. Same thing with this. They have made kilogram, put it in the same place, the same laboratory near Paris, it's sever, I think it's called. And well, 100 years later in 20th century they basically found that it's not exactly a kilogram. There are some micrograms difference or something like this. I don't know how they have discovered it, but basically it's obvious that things do change and the standard which we made ourselves cannot really be a real standard. We have to really base it on some physical constant. Now, which one? Now, this lecture is kind of more difficult to understand than the previous. The previous one with meter, that was kind of easy. Speed of light measured the time, one fraction, whatever the fraction is, or a second and that's the length covered by the light. With kilogram it was difficult. The first suggestion was let's measure exactly the mass of one particular atom of silicon, I believe. Well, silicon is basically abundant. That's sand basically, it's a silicon. So, let's take one particular atom and have a certain number of these atoms. If we know the weight, not the weight, the mass of one particular atom then we can multiply it so many times to have one kilogram and then we can say, okay, kilogram is the mass of so many atoms of silicon. Quite frankly for me personally that would be a very natural understanding of how we define the kilogram. For some reason that was rejected by physicists. Maybe one of the reason is that there are other isotopes of silicon, silicon 29 and silicon 30 with different number of neutrons in the nucleus. And maybe it's difficult to separate. I don't really know the reason. It was rejected. So, they decided to go along in my personal view a more kind of sophisticated way and they still did. I mean, they have decided to have some other physical constant, not the mass of atom, but some other physical constant which maybe was easier to measure, reproduce or whatever. I'm not really sure why. So, what is this? Okay, when we were talking about waves we were talking about the energy, the way it carries with it. And in particular there was an effect when the energy was carried in chunks called photons. And the energy of one photon was equal to some kind of a constant called Planck's constant times mu which is frequency of the wave, electromagnetic wave. So, this is the constant and this constant was calculated as being equal to 6.6267015 times 10 to minus 34 joules times second. Okay, so, now they have decided that this constant is better suited for definition of the mass. Well, first of all, what is joule? Joule is the energy measure and it's a kilogram meter second, I use s, second square. That's the force times distance, right? So, that's the definition of joule. And so, basically it's a kilogram here. The meter we know what meter is, we have already defined meter and second also we defined properly. Which means that if kilogram is defined then everything is defined and we have this constant. So, again, they made the reverse. Let's say that this constant is exactly equals to this particular number because, again, if we start from kilogram we can never have an exact number here. But if we start from the number, this number we will have the standard which fits this particular number for a kilogram. So, that's what the typical process of defining the new process of defining the units based on some constant is. So, the unit is such that we'll give exactly this constant as far as the calculations are concerned. So, first this constant was obtained experimentally with whatever units they had at the time. Whatever kilogram they have, whatever meter and whatever second. Now, since we are redefining this from the constant back to the unit we are saying, okay, our unit is such that delivers this particular number as a Planck's constant. Well, basically that's it. We have to define it which means we have to know how to, you know, have some experiment which delivers certain things based on this particular Planck's constant because we have postulated this Planck's constant. So, we know exactly what is the energy. If we know the energy, we can find what is the kilogram, basically. What is the mass of whatever we are dealing with. So, again, this is a very important philosophical change of defining units not based on our own kind of definition. I don't know, we have made an object and say this is a standard. We are taking a certain constant to be exactly some such a number and from this we derive the unit of measurement. Same thing as with time when we were saying that a certain number of oscillation is equal to one second. Same thing with lengths when we were saying that the distance covered by light in one fraction, whatever the fraction is of a second is the meter. Same thing here. Kilogram is whatever delivers this particular value to the Planck's constant. Now, the relationship between the energy here and the mass is very simple. That's Einstein's equation in relativity theory. So, these two, it's quantum physics and this is the theory of relativity. It's all something which is not really covered by this course. I just use the formulas basically as given. It's much more complicated parts of the physics. But anyway, the relationship between page and energy, relationship between energy and mass and that's how we get the mass unit. Now, if we have defined what is a kilogram obviously we have gram which is one thousandth of a kilogram. We have milligram which is one thousandth of a gram which is one millionth of a kilogram. We have microgram which is another thousand. Nanogram which is another thousand. Picogram which is another thousand of the previous. Every time we just divide it by a thousand. Now, going into multiples, we have a ton. By the way, the ton, there is a ton in the United States which is spelled like this. Now, this ton is spelled like this. So, this is exactly one thousand kilogram. And there is a kiloton, abbreviation is ton. There is a kiloton, there is a megaton and there is a gigaton. So, it's a thousand tons, million tons and billion tons. Alright, so basically that's it about mass. Again, don't miss the logic of this. First, we define something in time, unit of time which is a second. Using the second and speed of light we have defined the lengths. Now, using the second as a unit of time and meter as a unit of distance, we have defined unit of mass, kilogram, by postulating the Planck's constant. And that's always like this. We always preserve this logical connection. We define something and then based on this we define something. It's like proving theorems. We have axioms. Axioms are in this case equivalent to world constants, physical constants, natural constants. Then we have derived first kind of set of theorems from these axioms. Then the theorems from the theorems, etc., etc., by building the logical construction. Here is exactly the same thing. That's it for today. Thank you very much and good luck.