Quantum Mechanics Series – 4 : The Existence of Atoms

The Existence of Atoms

India Philosopher “Kanad” before 600 B.C. said that each matter consists of small particles which are called “Kan”. He gave those small particle his own name.

A Greek philosopher named Democritus (c. 460−370 B.C.) also first proposed the concept of atoms (means “indivisible” in Greek).

The idea was questioned by Aristotle and debated for hundreds of years before the English chemist John Dalton (1766 – 1844) used the atomic concept to predict the chemical properties of elements and compounds in 1806.

But it was not until a century later that a theoretical calculation by Einstein and experiments by the Frenchman Jean Perrin (1870−1942) persuaded the sceptics to accept the existence of atoms as a fact.

However, during the 19th century, even without physical proof of atoms, many theorists used the concept.

 

Averaging Diatomic Molecules

The Scottish physicist J.C. Maxwell, a confirmed atomist, developed his kinetic theory of gases in 1859.

 

This was qualitatively consistent with physical properties of gases, if we accept the notion that heating causes the molecules to move faster and bang into the container walls more frequently.

 

Maxwell’s theory was based on statistical averages to see if the macroscopic properties (that is, those properties that can be measured in a laboratory) could be predicted from a microscopic model for a collection model for a collection of gas molecules.

 

Maxwell made for assumptions :

Maxwell : gave distribution of velocity for gas particles

1. THE MOLECULES ARE LIKE HARD SPHERES WITH THEIR DIAMETERS MUCH SMALLER THAN THE DISTANCE BETWEEN THEM.

2. THE COLLISIONS BETWEEN MOLECULES CONSERVE ENERGY.

3. THE MOLECULES MOVE BETWEEN COLLISIONS WITHOUT INTERACTING AT A CONSTANT SPEED IN A STRAIGHT LINE.

 

 

 

 

This last assumption was the most unusual and revolutionary showing a great deal of physical insight by Maxwell.

It would be impossible by try to compute the individual motions of many particles. But Maxwell’s analysis, based on Newton’s mechanics, showed that temperature is a measure of the microscopic mean squared velocity of the molecules. 

The real importance of Maxwell’s theory is the prediction of the probable velocity distribution of the molecules, based on his model. In other words, this gives the range of velocities…how the whole collection deviates from the average.

Postulates of Maxwell Theory helps to calculate probability that a molecule chosen at random would have a particular velocity.

Maxwell velocity distribution curve:

This is the well known curve which physicists today call the Maxwell Distribution. It gives useful information about the billions and billions of molecules, even though the motion of an individual molecule can never be calculated. This is the use of probabilities when an exact calculation is impossible in practices.

 

 

 

 

Ludwig Boltzmann and Statistical Mechanics

In the 1870s, Ludwig Boltzmann (1844−1906) – inspired by Maxwell’s kinetic theory – made a theoretical pronouncement.

  • He presented a general probability distribution law called the canonical or orthodox distribution which could be applied to any collection of entities which have freedom of movement, are independent of each other and interact randomly.
  • He formalized the theorem of the equipartition of energy.

This means that the energy will be shared equally among all degree of freedom if the system reaches thermal equilibrium.

  • He gave a new interpretation of the Second Law.

 

When energy in a system is degraded (as Clausius said in 1850), the atoms in the system become more disordered and the entropy increases. But a measure of the disorder can be made. It is the probability of the particular system – defined as the number if ways it can be assembled from its collection of atoms.

More precisely, the entropy is given by :

          S = k Log W −−−−

Where k is a constant (now called Boltzamann’s constant) and W is the probability that a particular arrangement of atoms will occur. This work made Boltzmann the creator of statistical mechanics, a method in behavior of their constituent microscopic parts.