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Is energy quantized in classical physics?

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No,according to classical wave theory the emission of electromagnetic radiations from the surface is continuous. So energy is not quantized in classical physics.But according to photon theory the emission of electromagnetic radiation from the surface is discontinuous.Energy is quantized and radiations are emitted in the form of bundles of energy is called quanta or photon.Each photon has energy given as:

E  = h ν

Where h is Planck constant and ν is the frequency.

What is quantization of energy?

The assumptions made by Plank in deriving his radiation law and their consequences along with significance of Plank’s constant h were not immediately clear to his contemporaries and even to Plank himself.Plank derived his radiation law by analyzing the interaction between radiation in the cavity volume and the atoms of the cavity walls.He assumed that these atoms behave like tiny oscillator each with a characteristic frequency of oscillation.

These oscillations radiation energy into the cavity and absorb energy from it.As such,the characteristics of the oscillators that generation.

Classically ,the energy of the tiny oscillators has a smooth continuous behaviour or acts as a continuous variable.This continuous behaviour of energy can be assigned to large scale oscillators such as pendulums and mass spring systems.In order to derive Plank’s radiation law it is necessary to make a radical assumption e.g atomic oscillators may not emit or absorb any energy E in a continuous fashion but only in a discrete fashion defined by:

E =nhν   ,n=1,2,3    …………….(1)

Where ν is the oscillator frequency.We see that Plank’s constant h was introduced into physics for the first time in connection with quantization of energy of atomic oscillators and integer n is a quantum number.It follows from equation (1) that oscillator energy levels are evenly spaced with an interval of hν.

The assumption about quantization of energy is a radical one and Planck himself remained reluctant to accept it for many years.From experience we know that a pendulum can oscillate with any reasonable total energy and not only with certain related values.As friction causes the amplitude of the pendulum to decay it appears that energy of pendulum is dissipated in a continuous fashion but not in jumps or “quanta” .Since Planck constant is so small,the jump may be there but for too small for us to detect and hence we cannot dismiss energy quantization.

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