Do electrons have volume? How to measure?

The landlord asked this question, which seems to be a well-known scientific problem.

It should be clear that the objects we are talking about have "volume" are all macroscopic objects, macroscopic objects have obvious boundaries, such as a table, the surface is flat, this is clear, the surface down is the part that belongs to the table, and the surface up is the air, which does not belong to the table. If you throw it with a leather ball, it will inevitably hit the table after it will be **, and it is not ambiguous at all. Then the volume is very good to measure, and many conventional methods can do it.

But the electron is a microscopic, very mysterious thing, first of all, it is so small, and in many cases the motion does not obey Newton's laws, but has to be treated with quantum mechanics. In quantum mechanics, matter is wave-particle duality, which has the characteristics of both particles and waves, and it is difficult for you to say that you can hit the surface of something and bounce it back, although it has a similar effect but it is completely different, and there is no obvious boundary. And we look at general objects through light, and now electrons as microscopic objects can interact with photons, and it is impossible to look at them, take a ruler and measure them.

In short, you can say that volume is not measurable at the moment, or that its volume is not defined (we say that the concept of volume is for macroscopic objects with clear boundaries), and for electrons we have to redefine the concept of volume. Here's a redefined concept called "classic radius".

Upstairs gives the static mass of the electron, which can be measured. According to Einstein's mass-energy equation, it can be calculated that the energy e=mc and c is the speed of light. Then it can be seen as a stationary electron with so much energy as mc; In addition, from the perspective of electromagnetism, there is an electric field around the electron, the magnitude is e=ke r, the direction is pointing towards the electron, and it can be extended to infinity.

The electric field has energy, and the energy in the unit volume is 1 2 e ( is the dielectric constant), so the total energy can be obtained by integrating this energy with the volume of the whole space. However, it is not possible to start the integration from r=0, in that case the result is infinity and must be calculated from a certain r0. Logically speaking, mc is the energy possessed by the electron, and the integral of this energy density is also the energy possessed by the electron, and the two should be equal, and to make the two equal, r0 must be equal to a number, which is defined as the classical radius of the electron.

The volume can be understood as the volume of the sphere of this classical radius r0, 4 3 r0. That is to say, we no longer define the space occupied by an object as a volume, as is the case in the classical way, but define a volume for it from the perspective of energy.

However, the teacher recently said that the current research has not yet discovered the structure of the electron, that is, when the scale is much smaller than the classical radius r0 above, a series of experiments have been done, and the electron still has not been found to have an internal structure, as if it is still a point charge. Therefore, r0 is definitely not the boundary of an object in the classical understanding, and the interior of r0 cannot be regarded as belonging to the interior of the electron.

Of course, electrons also have volume, it's just that it's too small to be measured at the moment.

Different objects are calculated differently, for example, the cube of a cuboid is the volume: length, width, and height; The cube of the cube is the volume: edge length x edge length x edge length.

In terms of graphics, the cubic is a measurement of the volume of an object, such as cubic meters, cubic decimeters, cubic centimeters and other common units, the steps are as follows:

1) Find the edge length of the cube.

2) Ridge length = volume (Note: if the unit of edge length is centimeter, the volume unit is cubic centimeter, written cm; If the unit of edge length is meters, the unit of volume is Changxiao cubic meters, written m, and so on. ）

1）（a+b）³＝a³＋3a²b＋3ab²＋b³

2）a³+b³=a³+a²b-a²b+b³=a²（a+b）－b（a²-b²）＝a²（a+b）－b（a+b）（a-b）

a+b) a -b(a-b) = a+b) (rush a -ab+b).

3）a³-b³=a³-a²b+a²b-b³=a²（a-b）＋b（a²-b²）＝a²（a-b）＋b（a+b）（a-b）

a-b）［a²+b（a+b）］=a-b）（a²+ab+b²）

A method for measuring the volume of an object.

1. Objects that sink to the bottom of the water 1- The regular clear object is directly measured with a scale to measure the length of this forest a, width b, height c, v=abc; 2.Irregular objects are measured with a graduated cylinder, using the "drainage method", and the volume of the solid measured is v=v2-v33

Weighing method, Archimedes' principle, the object is hoisted on the dynamometer, the measured gravity is g, immersed in water, the number is f, then the v of the object is, v=(g-f) gpx4Fill the overflow cup with water, put the object into the overflow cup, collect the overflowed water into a small beaker, and measure the mass of the water m water with a balance, then v=mm p water.

2. The measurement of the volume of floating objects on the surface of the water is usually measured by the following two methods: a. acupressure (tool measuring cylinder, water, pin); Press the floater into the water with a pin and note the changes in the water of the graduated cylinder.

b。Sinking method (tool measuring cylinder, water, thin wire, stone. Pour an appropriate amount of water into the graduated cylinder, and then tie the metal block with a thin wire and put it into the water Zen Mausoleum to mark v, and then tie the metal block and the code attack float together and sink it in the water to write v2, v=vz-v1.

3. Substances that should absorb water: First, the outer surface of the object is coated with a thin layer of substances that are not easy to absorb water, such as paint; The second is to put the substance into the water first