Inadequacies of classical Mechanics

Inadequacies of classical Mechanics:

Classical mechanics describe the motion of the macroscopic particle, such as star, planet, moon, lump of clay as well as microscopic particle such as motion of a bacteria, virus. It describe the motion of a particle in non-relativistic limit. i.e. V<<C

Newtonian mechanics is based on concept of

1. Absolute Space
2. Absolute Time
3. Absolute mass and it's contained

In Newton's law of motion (\(\vec F= m\vec a\)). Due to certain limitation of classical mechanics and it's wrong assumption could not explain following physical phenomena.

1. It could not explain the spectrum of black body radiation.

According tot classical theory of radiation the energy density of black body radiation is

$$u(\nu, T)=\frac{8\pi\nu^2}{C^3} KT\dotsm(1)$$

At given frequency \(\nu\) and temperature T

Total energy density = \(\int_0^\infty u(\nu, T)d\nu\)

$$=\frac{8\pi KT}{C^3}\int_0^\infty \nu^2 d\nu$$

$$=\frac{8\pi KT}{C^3}\biggl[\frac{\nu^3}{3}\biggr]_0^\infty$$

$$=\inftty\;[ Ultraviolet; Catastrophe]$$

The total energy density at temperature T comes out to be infinity but experimentally T total energy should be finite and measurable.

2. It could not explain the stability of atoms.

According to classical theory electron accelerate around nucleus of an atom less it's energy in the form of radiation ad it's energy continuously decreases. Radius of electronic orbit also decreases and electron jump inside nucleus and atom becomes unstable.

But in real atom is stable.

3. It could not explain discrete atomic spectrum:

According to classical theory of radiation, energy exchange between atom and radiation field must be continuous. But atoms absorbs and emits discrete energy in unit of (\(h\nu\)).

4. It could not explain photoelectric effect:

According to classical theory of radiation the kinetic energy of emitted electron ( photoelectron ) depends upon the intensity of radiation, independent of frequency.

According to experimental observation of Einstein photoelectric effect, the kinetic energy of photoelectron depends upon frequency of incident radiation, independent of intensity. i.e.

$$h\nu=\phi_0 + \frac12 v^2\dotsm(2)$$

Where,

\(h\nu\)= energy of incident photon.

\(\phi_0\)= Work function

\(M_e\)= Mass of electron.

\(V\)= Velocity of electron.

For \(\nu>\nu_0=\frac{\phi_0}{h}= \) threshold frequency

$$K.E\propto h\nu$$

In classical mechanics we can't explain threshold frequency.

5. It could not explain the phenomena of pair production (\(E=mc^2\)).

6. It could not explain the phenomena of Compton scattering.

According to classical theory of radiation the frequency of scattered radiation should be equal to frequency of oscillating charge (electron), which is equal to frequency of incident radiation. There should be no change in frequency.

$$d\nu=0$$

$$d\lambda=0$$

According to Compton effect the observed shift in wave length of scattered radiation is given by,

$$d\lambda=\lambda'-\lambda=\frac{h}{m_0 c}(1-cos\theta)$$

Where,

\(\lambda'\)= Wavelength of scattered radiation.

\(\lambda\)= Wavelength of incident radiation.

\(h\)= Planck's constant

\(m_0\)= Rest mass

\(\theta\)= Angle of incident radiation

\(d\lambda\)= \frac{h}{m_0 c}= Constant = 0.0243\(A^0\)

7. It could not explain variation of electric conductivity of solid ( supper conductivity ).

8. Classical mechanics could not explain the phenomena associated with spinning motion of electron. ( Ferromagnetism, Poulies exclusion principle ).

9. Classical mechanics could not explain Zeeman effect, Stark effect, Raman effect.

10. It could not explain phenomena of radioactivity (\(\beta\)-decay, \(\alpha\)- decay )

11.Classical mechanics is based on the exact measurement of physical quantity but in real we can not measure a physical quantity exactly and preciously with out any error ( uncertainity pricipel ).

12. According to classical mechanics total energy of particles is always positive. But in Dirac theory negative energy state is also exit. ( Existance of positron, antiparticle of electron). The energy of positron is negative before it's formation. So this can not explain by classical theory.

To sole above physically observable problem Scientists purposed, a new field of physics based on uncertainity principle and wave-matter duality of particles. This new field of physics is known as quantum mechanics.

Reference:

1. Mathews, P.M and K Venkatesan. A Text Book of Quantum Mechanics. New Delhi: Tata McGraw Hill Publishing Co. Ltd, 1997.
2. Merzbacher, E. Quantum Mechanics . New York: John Wiley, 1969.
3. Prakash, S and S Salauja. Quantum Mechanics. Kedar Nath Ram Nath Publishing Co, 2002.
4. Singh, S.P, M.K and K Singh. Quantum Mechanics. Chand & Company Ltd., 2002.