__Introduction __

__Introduction__

The __ History of Development of quantum physics__ takes place at the beginning of 1900. It is also called wave mechanics. Quantum physics is highly

In this article, we are going to discuss various important topics related to the development of *quantum physics* along with failures of classical mechanics. Before starting the discussion about the development of quantum physics, it’s important to know that why this branch of physics was developed. We will discuss several theories by different physicists, their assumptions, and results. History of Development of quantum physics has an great importance in the world of physics.

__Failures of classical mechanics__

1. The classical theory doesn’t fall in the region of atomic dimension. It cannot explain the non-relativistic motion of atoms, electron, protons (v<<c)

2. It cannot explain the observed spectrum of blackbody radiation.

3. It cannot explain the stability of atoms.

4. It cannot explain the variation of the Specific heat of metals and gaseous

5. It cannot explain the various phenomena like the photoelectric effect, quantum effect, Raman effect.

6. It cannot explain the origin of discrete spectra of atoms. Because classical mechanics energy changes are always continuous.

In order to overcome these failures, *quantum physics* was* developed.*

__Theories of History of Development of quantum physics__

The History of Development of quantum physics Consists of many important theories based on different- different assumptions. Like,

1. Planck’s hypothesis:-

according to Planck’s a harmonic oscillator could have the energy of an integral multiple of hf(f=frequency).

2. Bohr’s hypothesis:-

According to Bohr angular momentum of an electron orbiting in an atom is an integral multiple of ħ ie h/2π

3. Einstein assumption:-

Einstein assumes that in the interaction of light with matter, the energy of light is assumed to be in form of bundles of energy hν.

__Black body radiation in terms of quantum law of physics__

__Black body radiation in terms of quantum law of physics__

1) The energy is not uniformly distributed in the energy spectrum of a black body.

2) At the given temperature the intensity of radiation increases with the increment in wavelength. And becomes maximum at a particular wavelength. By further increasing wavelength intensity decreases.

3) As the temperature increases, cause a decrement in λm (maximum value) i.e. λm is directly proportional to 1/T.

λmT = constant

λmT = b

Where b is Wien’s constant 0.293× 10-2, Wien’s displacement law.

4) The increment in temperature causes an increment in energy emission on all wavelength.

5) The area under each curve represents the total energy emitted by the body at a particular temperature.

E is proportional to T4.

E = σT4

σ Stephen’s constant

__Wein’s formula:- __

Uλdλ = A/λ5 e-B/λT dλ

A and B = constant

__Wein’s formula:-__

This law only applies to the shorter wavelength. For a smaller value of λ, exponential term is large and contributes more .so that uλ increases with λ. But for a larger value of λ (longer λ ) exponential term is small thus λ5 factor dominates mostly i.e. Uλ decreases with λ.

__Rayleigh and jeans law__

__Rayleigh and jeans law__

according to Rayleigh and jeans law:-

Uλdλ= 8πKT dλ/λ⁴

Rayleigh and Jean’s law agree with the longer wavelength. As we mover towards shorter wavelength or UV rays the resultant energy would increase without any limit. This prediction is called ultraviolet or UV catastrophe andEλdλ = ∫ 8πKT dλ / λ⁴ is tends to ∞.

__Plank’s hypothesis and plank’s radiation law__

Plank’s assumes that –

1. The atoms of the wall of the cavity radiator behave as the oscillator.

2. This oscillator emits electromagnetic radiant energy into the cavity. Also, absorb the same from it. And in this way, it maintains the equilibrium state

3. An oscillator can have only discrete energy E = nhv where n is integer number.

4. The oscillator doesn’t emit energy. As well as it doesn’t absorb energy continuously .but only in jumps or packets. Each packet carries hv energy.

** Derivation** :-

**Derivation**Let N₀ , N₁, N₂,N₃ ,…..are the numbers of oscillators having the energies 0 ,hv, 2hv ,…..then in general-

Nr = N₀ e-rhv/kt (__Maxwell Boltzmann’s rule__)

total number of oscillators are ,

N = N₀ + N₁ + N₂ + …..

Also, N = N₀+ N₀ e-hv/kt + N₀ e-2hv/kt + ….

i.e. N = N₀(1 + e-hv/kt + e-2hv/kt + …)

** N= N₀/ 1- ehv/kt**

Total energy of the oscillator,

E = N₀×0 + N₁× hv + N₂×2hv + ……

E = N₀ hv / 1-e hv/kt + N₀ 2hv/ 1-e hv/kt + N₀ 3hv/ 1-e hv/kt….

E= N₀ hv e-hv/kt [1+ 2e-hv/kt +3e-2hv/kt ]

** E= N₀ hv e-hv/kt hv/ (1-e hv/kt)²**

Now dividing above equation we get –

E/N = e-hv/kt hv (1- e-hv/kt)/ ( 1-e -hv/kt)²

Or,

** E/N = hv /(eh/kt-1)**

Which is the required result

Hence ,in order to acquire knowledge about failures of classical mechanics ,we are now able to understand the importance of “**History of Dovelopment of quantum physics**“.