 ## How to Measure Small Things

Measurement of vast distances is a straightforward job. We use large units of length such as kilometres for inland applications, light years for stellar applications and 1 parsec (3.26 light-years) for intergalactic applications. On another end of the scale, we have minimal measures. We can only understand millimetres and our naked eyes can sense up to 0.1 mm, but after that, it becomes tough to visualize. We have only recently begun to explore and understand the miniature world out there with modern technological development. To measure small things, we need to understand the Avogadro number and his hypothesis to know and how to measure the small distances.

An electron microscope is a particular type of microscope that illuminates the sample with a beam of accelerated electrons. This electron will be needed to have a very short wavelength, approximately 100,000 times shorter than the visible light, hence, giving the electron microscope a better resolution characteristic than an optical microscope. This can be heavily used to observe tiny things such as atoms and molecules. A transmission electron microscope can extensively achieve better than 50 Picometer (10-12) resolution, and we should also remember that atoms range from 30 – 300 Pico meters. There is another interesting fact that the radius of an atom is approximately more than 10000 times the radius of the nucleus and the atom is 99.999999% space. Before any of the technological advancements in the peripheries, we had only come to know about the rough estimate of the size of the atom even after the Rutherford alpha particle which on scattering experiment gave us the size of the nucleus in an approximate measurement. Now, we have to understand some of these methods about how to measure small things.

The actual volume which is occupied by the particular atom of a substance is every timeless than the volume of that important substance because the packaging of atoms is inefficient. Due to this, there are empty spaces between atoms which results in an inflated volume. According to Avogadro's number, the actual volume which is occupied by the particular atoms in a certain mass of a denoted substance is two-thirds the volume which is occupied by that mass of the substance. Suppose if we take a mole of a substance, let us say Carbon. A mole generally refers to the amount of the substance in grams which is equivalent to the atomic weight of the substance. So if we keep talking of Carbon, one mole of Carbon consists of 12 g of pure carbon-12 (12C). There is another interesting fact about Avogadro's number unit that is: the definition of Avogadro's number is the same as of a mole which is given as the Avogadro uses Carbon as the standard for mole.

We previously know that volume is the ratio of mass divided by density. We can easily calculate the atomic volume of the whole mole.

Molar Volume = Molar Mass (gm)/ Density (gm/cm3)

### Solved Examples

1. How is Avogadro's Number Used?

The mole system allows the scientists to accurately calculate the number of elementary entities (usually atoms or molecules) in a particular mass of a given substance. Avogadro's number is absolute and constant: there are 6.022×1023 elementary particles in one mole. This can extensively be written as 6.022×1023 mol-1.

### Did You Know?

This is a fantastic fact that Amedeo Avogadro comes into the territory, of course, his real name is Lorenzo Romano Amedeo Carlo Avogadro di Quaregna e di Cerreto—but everyone calls him Avogadro for apparent reasons. Avogadro developed the idea which is given:

If we think that Avogadro just introduced just a version of the Ideal Gas Law, then we are correct—but we have to move on to a useful example. Suppose if we take water (that is H2O) and run a short streak of electric current through it, it is called electrolysis. This process can easily break the water molecules into hydrogen gas and oxygen gas (which we could collect). If we had these two gases at the same temperature and pressure, the hydrogen gas would surely take up twice the volume compared to the oxygen gas. Why? Well, when we have to break up the water molecule, we get twice as much hydrogen as oxygen.

1. How Can We Measure The Diameter Of A Carbon Atom?

A mole which is defined by the Avogadro's number definition has 6.02 x 1023 elementary particles. By using this method, we can obtain the approximate atomic volume of the carbon atom.

Atomic volume = Molar Mass ( in gm)/ [Density ( in gm/cm3) x Avogadro Number]

Carbon Atomic Volume = 12 (in gm)/ [(2 in gm/cm3) x) 6.02 x 1023)]

We should also remember how to introduce the two-thirds law discovered by Avogadro.

Carbon Atomic Volume = [2 x 12 (in gm)]/ [3 x (2 in gm/cm3) x) 6.02 x 1023)] = 6.6467 x 10-24 in cm3. If we Calculate the diameter, we get an accurate value of Diameter of Carbon = 0.116 nm.

But this is not entirely correct. This value is a little and way too small. The elementary atom diameter ranges from 0.3 nm that is 30 pm and hence this was the first considerably accurate estimate ever made. This is the thing which made the explanation of Avogadro hypothesis exciting.

2. What is The Conversion Of Avogadro's Number?

In other measurement systems present in the world, where the unit of substance is not only the SI mole, the Avogadro constant NA is taken to mean the number of particles in said unit, and we would have a different value.

For example, we can take, if quantities of a substance are to be measured in pound-mole (lb-mol), then the Avogadro constant NA is 2.73159734(12)×1026 lb-mol−1. If the ounce-mole (oz-mol) is to be used in place of that, NA is 1.707248434(77)×1025 oz-mol−1. However, these units are not used so much nowadays. This is where the definition of Avogadro's number can be clearly understood.