In the last lesson we talked about the relative atomic mass, which is actually the ratio of mass between atoms, so with this thing, we only need to know the mass of one of the atoms, we can calculate the mass of other atoms.
If we know the mass of hydrogen atoms, we can calculate the true mass of hydrogen atoms by multiplying their mass by the relative atomic mass of other atoms. So the next question is how do we calculate the mass of the hydrogen atom.
One way, in the mid-19th century, decades before Thomson discovered electrons, Faraday measured the ratio of atomic mass and unit charge in electrolysis experiments, for example, the ratio of mass and unit charge of hydrogen atoms was 1.044×10^-8 kg/coulomb.
At that time, Faraday did not know what this unit charge was, only that it was the smallest unit charge that ions could gain and lose in the process of electrolysis, and after Thomson discovered the electron, we knew that this was the charge carried by the electron. The charge value of each electron is the unit charge.
So now the key question becomes what is the charge of the electrons? All problems can be solved by asking for this value, so after Thomson discovered the electron, the most important work of the Cavendish laboratory under his command was to measure the charge of the electron.
Okay, let's start with the measurement of the electron charge, and then we'll talk about Faraday's electrolysis experiment.
Before talking about electron charges, we first understand one thing, Wilson cloud chamber, Wilson is Thomson's student, in the Cavendish laboratory, Wilson found that no dust particles are needed, charged particles can also be used as condensation nuclei to make the water vapor in the air condense into small water droplets, the discovery of this phenomenon means that we can use the condensation of dustless supersaturated water vapor to show the trail of charged particles.
So Wilson invented the cloud chamber accordingly, which allows us to clearly see the existence of subatomic particles, this device made a great contribution to the early development of particle physics, and later we invented a lot of similar equipment, such as latex photography, bubble chamber, spark chamber, multi-filament proportional chamber and so on.
The measurement of the electron charge is carried out in the cloud chamber, the first person to measure is Cavendish Laboratory Townsend, it is Thomson's colleague, the basic principle of measurement is this, the charged ions will condense into small water droplets when they pass through the cloud chamber, measure the charge-to-mass ratio of these small water droplets, and then measure the mass of the water droplets, you can calculate how much the charge carried by the ions is, and then according to the charge of the ions, you can know the charge value of the electrons.
Although charged particles form water droplets in the cloud chamber, these droplets are still too small to be measured directly, so find other ways to indirectly measure the quality of water droplets.
Townsend uses the method of measuring the speed of the water droplets falling under the action of gravity, to calculate the mass of the water droplets, the process is actually very simple, we know that the water droplets will first do acceleration movement under the action of gravity, with the increase of speed, the viscous resistance of the air will continue to increase, until the gravity is offset, this time the water droplets will fall at a uniform rate.
According to Newton's second law, we can know that the gravity of the water droplet = the mass of the water droplet × 9.8 m/s², the viscous resistance of the air is proportional to the radius and velocity of the water droplet, in 1851, Stokes has given the viscous resistance formula:
The viscous resistance acting on the water droplet = 6πη × the radius of the water droplet × the velocity of the water droplet, where η is the viscosity coefficient of the air, which measures about 1.82×10^-5 N/m².
When the water droplet falls at a uniform speed, the mass of the water droplet × 9.8 m/s² = 6πη× the radius of the water droplet × the speed at which the water droplet falls at a uniform speed. This velocity can be measured, so the relationship between the mass and radius of the water droplets can be known through this formula.
There is also a relationship between the mass and radius of the water droplets, that is, the mass of the water droplets = 4π/3× the radius of the water droplets ³ × the density of the water, and finally Townsend calculates the average mass of the water droplets in the cloud chamber.
Now what we need to know is that the mass of all the water droplets in the cloud chamber and the amount of charge they carry, the method used by Townsend is that all the water droplets are absorbed with sulfuric acid, and the charge in them, the charge and mass obtained by sulfuric acid can be measured, because the charge and mass carried by each water droplet are the same, so the ratio of the measured value is the charge-to-mass ratio of each water droplet.
We have just calculated the average mass of the water droplets, so Townsend's measurement in 1897 was that the charge value of the positive ion was 0.9× 10^-19 coulombs, and the charge value of the negative ion was 1×10^-19 coulombs, and the difference between the two data was 10%, which can be explained as the uncertainty of the experimental data.
In 1898 Thomson also measured the charge of the electron, and townsend used the method is basically the same, the difference is that the ions in the Thomson cloud chamber are generated by X-ray irradiation of air, he did not use sulfuric acid when measuring the total mass of the water droplets and the total charge, and by measuring the conductivity of the air and the change in temperature, indirectly measured the charge-mass ratio on the water droplets, the final result was 2×10^-19 coulombs, 1901 experiments were improved, Thomson cited values of 1.1×10^-19 coulombs.
In 1903, Wilson continued to follow, and also measured the charge of electrons, and he measured the radius and mass of the water droplets, as mentioned above, by measuring the falling speed.
The difference is that after Calculating the mass and size of the water droplets, Wilson applied a uniform electric field to the cloud chamber, at which time the water droplets were subjected to three forces, gravity, air viscous resistance, and electric field forces.
Gravity can be calculated according to the mass just calculated, viscous resistance can be calculated according to the radius of the water droplet and the speed of observation, and the electric field force is equal to the charge on the water droplet multiplied by the electric field strength.
When these three forces are balanced again, the water droplets will fall at a uniform rate, and then we can calculate the charge of the only unknown amount of water droplets, which Wilson measured in 1903 was 1.03×10^-19 coulombs.
It can be seen that the consistency of the three results is very high, but people still feel that there is a problem with this experiment, the error is always very large, and the measured value is not accurate, so in 1906, the American physicist Mirigan decided to re-measure the charge of the electron, and he hoped to get more accurate results than the Covindisch laboratory.
In the Millikan experiment, the biggest improvement is that he did not use water vapor, but used mineral oil, so called the Milligian oil drop experiment, he used a sprayer to spray mineral oil into the cloud chamber, the oil droplets formed around the charged ions have two characteristics, first of all, the surface of the oil droplets is not easy to evaporate, so the quality can always be guaranteed, the second is in the water vapor experiment, we can only see a cloud, can only study the cloud as a whole, but the mineral oil is not the same, we can see a single oil droplet in the cloud chamber, So it can be tracked.
For example, we can apply an electric field to the cloud chamber, let a certain oil droplet rise, and then remove the electric field, let it fall, in the process of multiple rises and falls, we can accurately measure it, and finally calculate its charge.
Let's say that one of the examples of the 1911 Mirigan paper, no. 6 oil droplet, when no electric field is applied, the no. 6 oil droplet has a velocity of 8.59 ×10^-4 m/s under the condition of uniform falling, and the calculated oil droplet mass is 8.10×10^-14 kg, and the radius is 2.76×10^-6 meters.
Then add an electric field with a strength of 3.18×10^5 V/m to the oil droplet, the reverse of the electric field force is opposite to the direction of gravity, and when the oil droplet begins to rise at a uniform speed, it means that the upward electric field force and gravity and the sum of viscous resistance have reached a balanced state.
At this time, we can list a formula, the formula is only an unknown amount of oil droplet charge, here I will not write the formula, directly give the result. By measuring the upward velocity, we can calculate that the charge of this rising oil droplet is 29.87×10^-19 coulombs.
Then we remove the electric field, let the oil droplets fall, and then add the electric field, measure the charge of the oil droplets again, remove the electric field again, add the charge, continue to measure, repeat many experiments, we get a set of data.
29.87, 39.86, 28.25, 29.91, 34.91, 36.59, 28.28, 34.95, 39.97, 26.65, 41.74, 30.00, 33.55, these values are all in units of 10^-19 coulombs.
It can be seen that these numbers are much larger than the charge of the electron, so this is not the charge of the electron, nor is it a unit charge, and it is difficult to see what the law is between them, don't worry, we first take the difference between them, that is, with the charge of the oil droplet minus the charge of the previous rise, we can get a foot of charge change data.
9.91, -11.61, 1.66, 5.00, 1.68, -8.31, 6.67, 5.02, -13.32, 15.09, -11.74, 3.35, from their differences, it can be seen that each change in charge is an integer multiple of the minimum amount, and it can be calculated that this smallest charge is about 1.665×10^-19 coulombs
This value is the smallest unit charge, is the charge value of the electron, this is the result of the measurement of the No. 6 oil droplet, then after Milligan repeated the above measurements on multiple oil droplets, the average electronic charge obtained is 1.592×10^-19 coulombs.
This value is very accurate, and Townsend, Thomson, and Wilson used water vapor to measure the average of the ion charges in the entire cloud, so it is not accurate.
Well, now that we have the charge of the electron, we can figure out the mass of the electron, as well as the mass and volume of the atom. Before we do that, let's talk about the ratio of the mass of atoms to the unit charge.
Humans found that the electrolysis phenomenon began with water, but also inadvertently saw that the two poles of the wire can produce hydrogen and oxygen in water, then Faraday conducted an in-depth study of this phenomenon.
Take water, now we know that this is because there are charged ions in the water, including positively charged hydrogen ions and negatively charged hydroxide ions, when two electrodes extend into the water, the positively charged hydrogen ions will be attracted to the negative electrode, and then get two electrons, it becomes hydrogen, the negatively charged hydroxide ions run to the positive electrode, they will lose four electrons, become two water molecules and an oxygen molecule.
This is the process of electrolyzing water, from which Faraday found that at any current intensity, the mass of oxygen generated is always 8 times the mass of hydrogen, but the relative molecular mass of oxygen is 16 times that of hydrogen, which means that the rate of hydrogen production is 2 times that of oxygen. Faraday then deduced that it takes two units of charge to generate hydrogen, and four charge charges to generate oxygen. As we now know it.
Faraday's guess was also correct when electrolyzing silver chloride, requiring one unit of charge to generate silver atoms and 2 units of charge to generate chlorine.
Although Faraday did not know the mass of the individual atoms at this time, and what the unit charge was, it was possible to calculate their ratio.
For example, when electrolyzing silver chloride, it can be known by weighing the silver deposited on the cathode, and the current of 1 ampere can produce 10^-6 kg of silver in 1 second.
Since a unit of charge can produce a silver atom, the number of silver atoms generated is equal to the number of unit charges flowing through 1 ampere of current in 1 second.
According to the definition, the total amount of charge flowing through an ampere of current in 1 second is 1 coulomb, so 1 coulomb/unit charge = 10^-6 kg/mass of silver atoms, so the ratio of the mass of the silver atom to the unit charge is 10^-6 kg/coulomb.
We now know that the relative atomic mass of the silver atom is about 108 times the relative atomic mass of hydrogen, so the ratio of the mass of the hydrogen atom to the unit charge is 10^-8 kg/coulomb.
There is another way of calculating, any substance in a mole we said last time has the same number of molecules, which means that the amount of charge required to generate any substance with 1 mole at the time of electrolysis is equal to the number of unit charges required for each molecule (for example, hydrogen requires 2 units of charge, oxygen needs 4) multiplied by Faraday's constant, which is actually the unit charge amount (the unit charge amount is the charge value of the electron) multiplied by the Avogadro constant.
For example, to generate 1 mole of hydrogen, the total amount of charge required is 2× Faraday's constant, and a mole of hydrogen weighs two grams, so we can calculate the Faraday constant by measuring how much electricity is consumed to produce 2 grams of hydrogen.
At the end of the 19th century, the Faraday constant was measured at about 96580 libraries/mo, and with this constant we can know the mass of hydrogen atoms and the ratio of unit charge.
The relative atomic mass of our hydrogen is 1.008, so the hydrogen atom of 1 mole weighs 1.008 grams, or 1.008 × 10^3 kilograms, and then divide this number by Faraday's constant, and the result is 1.044×10^-8 kg/coulomb, which is the ratio of the mass of the hydrogen atom to the unit charge.
Now Mirigan measured the charge value of the electron, which is the size of the unit charge, so we multiplied the charge of the electron by 1.592×10-19 coulombs by 1.044×10^-8 kg/coulomb, so we calculated that the mass of the hydrogen atom was 1.663×10^-27 kg.
Of course, we can also calculate that the mass of the electron is 9× 10^-31 kg through the mass-to-charge ratio of the electron. It is also possible to calculate the Avogadro constant, using the charge value of the electron divided by the Faraday constant measured by electrolysis, and the final result is that the number of molecules per mole of matter is 6.062×10^23, which is the result given by Mirigan that year, and is not much different from today's accurate measurements.
Knowing the mass of the hydrogen atom, the mass of other atoms can be calculated by the relative atomic mass, and now we will estimate the size of the atom, taking the gold atom.
The relative atomic mass of the gold atom is 197, so the calculated mass is 3.25×10^-25 kg, and the density of gold is 1.93×10^4 kg/m³, so there must be 1.93 × 10^4/3.25 × 10^-25 gold atoms per cubic meter of gold, and the result is 5.94×10^28 gold atoms.
Thus each gold atom occupies a volume of 1/5.94×10^28, and the final result is 1.68×10^-29 m³, and the diameter is 2.6×10^-10 m.
See, as long as the charge of the electron is calculated, and finally the diameter of the atom is calculated, this is the charm of science. It's amazing.
The electron charge we accurately measured today is 1.601765×10^-19 coulombs, which is measured after the new air viscosity coefficient is used.
Although we are no longer measuring the charge value of electrons today, the oil drop experiments in Mirigan are still being done, because the quark model tells us that the charge carried by the electron is not the most basic unit of charge, and two quarks in the proton have -2/3 times the electron charge and 1 quark has 1/3 times the electron charge.
So people hope to find these charges in the experiment, proving that the quark is not just a theoretical model, and there have been sporadic reports that oil droplets with 1/3 of the electron charge have been found in the experiment, but this claim has not been widely confirmed.
So the current experiments have proved that the color confinement of quarks means that there are no free quarks. Well, the topic of quarks, which we'll talk about later, that's it for today.