MICROSCOPIC SCALE: PROPERTIES, COUNTING PARTICLES, EXAMPLES - PHYSICAL - 2025

The microscopic scale is one that is used to measure sizes and lengths that cannot be seen with the naked eye and that are below a millimeter in length. From highest to lowest, the microscopic scales in the metric system are:

- The millimeter (1 mm), which is one-tenth of a centimeter or one-thousandth of a meter. In this scale we have one of the largest cells in the body, which is the ovum, whose size is 1.5mm.

Figure 1. Red blood cells are cells on a microscopic scale. Source: pixabay

- The tenth of a millimeter (0.1 mm). This is the scale of the thickness or diameter of a human hair.

- The micrometer or micron (1μm = 0.001mm). On this scale are plant and animal cells and bacteria.

Plant cells are of the order of 100μm. Animal cells are ten times smaller, it is of the order of 10μm; while bacteria are 10 times smaller than animal cells and are of the order of 1μm.

Nano scale

There are measurements even smaller than the microscopic scale, but they are not commonly used except in some special contexts. Here we will see some of the most important nanometric measurements:

- The nanometer (1 ηm = 0.001 μm = 0.000001 mm) is one millionth of a millimeter. On this scale are some viruses and molecules. Viruses are on the order of 10m and molecules on the order of 1m.

- The angstrom (1Å = 0.1ηm = 0.0001μm = 10 ^-7 mm). This measurement forms the scale or atomic size.

- The phantomometer (1fm = 0.00001Å = 0.000001ηm = 10 ^-12 mm). This is the scale of atomic nuclei, which are between 10,000 and 100,000 times smaller than the atom. However, despite its small size, the nucleus concentrates 99.99% of the atomic mass.

- There are smaller scales than the atomic nucleus, since these are made up of particles such as protons and neutrons. But there is more: these particles are in turn made up of more fundamental particles such as quarks.

Instruments for microscopic observation

When objects are between the millimeter and micrometer scales (1mm - 0.001mm), they can be observed with an optical microscope.

However, if the objects or structures are between nanometers and Angstroms, then electron microscopes or the nanoscope will be required.

In electron microscopy, instead of light, high-energy electrons are used that have a much shorter wavelength than light. The disadvantage of the electron microscope is that it is not possible to place live samples in it because it works under vacuum.

Instead, the nanoscope uses laser light, and it has the advantage over electron microscopy that the structures and molecules within a living cell can be viewed and etched.

Nanotechnology is the technology with which circuits, structures, parts and even motors are manufactured on scales ranging from the nanometer to the atomic scale.

Microscopic properties

In physics, in a first approximation the behavior of matter and systems is studied from the macroscopic point of view. From this paradigm matter is an infinitely divisible continuum; and this point of view is valid and appropriate for many situations in everyday life.

However, some phenomena in the macroscopic world can only be explained if the microscopic properties of matter are taken into account.

At the microscopic point of view, the molecular and atomic structure of matter is taken into account. Unlike the macroscopic approach, on this scale there is a granular structure with gaps and spaces between molecules, atoms and even within them.

The other characteristic from the microscopic point of view in physics is that a piece of matter, no matter how small, is composed of a huge number of particles separated from each other and in continuous movement.

-The matter is an immense void

In a small piece of matter, the distance between atoms is enormous when compared to their size, but in turn the atoms are enormous when compared to their own nuclei, where 99.99% of the mass is concentrated.

That is, a piece of matter on the microscopic scale is a huge vacuum with concentrations of atoms and nuclei that occupy a very small fraction of the total volume. In this sense, the microscopic scale is similar to the astronomical scale.

From macroscopic objects to the discovery of the atom

The first chemists, who were the alchemists, realized that the materials could be of two types: pure or compound. Thus the idea of ​​chemical elements was arrived at.

The first chemical elements discovered were the seven metals of antiquity: silver, gold, iron, lead, tin, copper, and mercury. Over time, more were discovered as substances were found that could not be decomposed into others.

Then the elements were classified according to their properties and characteristics in metals and non-metals. All those that had similar properties and chemical affinity were grouped in the same column, and thus the periodic table of the elements emerged.

Figure 2. Periodic table of the elements. Source: wikimedia commons.

From the elements, the idea of ​​atoms was changed, a word that means indivisible. A short time later, scientists realized that atoms did have a structure. In addition, the atoms had two types of electrical charge (positive and negative).

Subatomic particles

In Rutherford's experiments in which he bombarded the atoms of a thin gold plate with alpha particles, the structure of the atom was revealed: a small positive nucleus surrounded by electrons.

Atoms were bombarded with more and more energy particles and is still being done, in order to unravel the secrets and properties of the microscopic world on a smaller and smaller scale.

In this way, the standard model was reached, in which it is established that the true elementary particles are those of which atoms are composed. In turn, atoms give rise to elements, these to compounds, and to all known interactions (except gravitation). In total there are 12 particles.

These fundamental particles also have their periodic table. There are two groups: the ½-spin fermionic particles and the bosonic ones. The bosons are responsible for the interactions. The fermionics are 12 and are those that give rise to protons, neutrons and atoms.

Figure 3. Fundamental particles. Source: wikimedia commons.

How to count particles on a microscopic scale?

Over time, chemists discovered the relative masses of the elements from precise measurements in chemical reactions. Thus, for example, it was determined that carbon is 12 times heavier than hydrogen.

Hydrogen was also determined to be the lightest element, so this element was assigned relative mass 1.

On the other hand, chemists required to know the number of particles involved in a reaction, so that no reagent is over or missing. For example, a water molecule requires two hydrogen atoms and one oxygen.

From these antecedents the concept of mole is born. A mole of any substance is a fixed number of particles equivalent to its molecular or atomic mass in grams. Thus it was determined that 12 grams of carbon have the same number of particles as 1 gram of hydrogen. That number is known as Avogadro's number: 6.02 x 10 ^ 23 particles.

-Example 1

Calculate how many gold atoms are in 1 gram of gold.

Solution

Gold is known to have an atomic weight of 197. This data can be found on the periodic table and indicates that a gold atom is 197 times heavier than hydrogen and 197/12 = 16,416 times heavier than carbon.

One mole of gold has 6.02 × 10 ^ 23 atoms and has the atomic weight in grams, that is, 197 grams.

In a gram of gold there are 1/197 moles of gold, that is 6.02 × 10 ^ 23 atoms / 197 = 3.06 x10 ^ 23 gold atoms.

-Example 2

Determine the number of molecules of calcium carbonate (CaCO ₃) in 150 grams of this substance. Also tell how many calcium atoms, how many carbon and how many oxygen are in this compound.

Solution

The first thing to do is determine the molecular mass of the calcium carbonate. The periodic table indicates that calcium has a molecular weight of 40 g / mol, carbon 12 g / mol, and oxygen 16 g / mol.

Then the molecular mass of (CaCO ₃) will be:

40 g / mol + 12 g / mol + 3 x 16 g / mol = 100 g / mol

Every 100 grams of calcium carbonate is 1mol. So in 150 grams they correspond to 1.5 moles.

Each mole of carbonate has 6.02 x 10 ^ 23 carbonate molecules, so in 1.5 moles of carbonate there are 9.03 x 10 ^ 23 molecules.

In short, in 150 grams of calcium carbonate there are:

- 9.03 x 10 ^ 23 molecules of calcium carbonate.

- Calcium atoms: 9.03 x 10 ^ 23.

- Also 9.03 x 10 ^ 23 carbon atoms

- Finally, 3 x 9.03 x 10 ^ 23 oxygen atoms = 27.09 x 10 ^ 23 oxygen atoms.

References

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2. Chemical Education. Macroscopic, submicroscopic and symbolic representations on matter. Recovered from: scielo.org.mx.
3. García A. Interactive physics course. Macro-states, microstates. Temperature, Entropy. Recovered from: sc.ehu.es
4. The microscopic structure of matter. Recovered from: alipso.com
5. Wikipedia. Microscopic level. Recovered from: wikipedia.com