3. Planck Length

In physics, the Planck length, denoted as ℓₚ, is a unit of length that is the distance by which a light travels in one unit of Planck time. It is a base unit in the system of Planck units. The Planck length can be defined from three fundamental physical constants and they are the speed of light in a vacuum, the Planck constant and the gravitational constant. What Planck did to get the Planck length is a clever bit of calculation. He first considered general relativity with two constants of nature : G (the gravitational constant) and c (the speed of light) and on the other hand, he also consider the quantum field theory with two constants : c (the speed of the light) and h (Planck's constant. Later, he attempted to unite these theories into one theory of quantum gravity as explained as below.

The units of G = (distance x distance x distance) / (mass x time x time).

The units of c = distance / time.

The units of h = (distance x distance x mass) / time.

Then Planck observed that there is only one way to combine these constants to obtain a distance which was equal to : 
 ℓₚ = √((h×G)/c³).

The resulting distance is called the Planck length. It means the distance at which the effects of quantum gravity will become apparent and may even be the smallest meaningful length that exists in the universe.

By solving the above will show the approximate equivalent value of this unit with respect to the meter:

1 ℓₚ ≅ 1.616229 × 10^⁻³⁵ m.

The Plank length is about 10^⁻²⁰ times the diameter of a proton. It can be defined using the radius of the hypothesized “Planck Particle”. Hence, like as this method, Max Planck, in 1819, suggested that there existed some fundamental natural units for length, mass, time and energy. These were derived by him using the dimensional analysis by using the universal physical constants such as the gravitational constant G, the speed of light c, and the Planck's constant h. The natural units he further derived became known as the “Planck length”, the “Planck mass”, the “Planck time” and the “Planck energy”.