Class 12 Physics Dual Nature Radiation Matter Heisenbergs Uncertainty Principle

Heisenberg’s Uncertainty Principle:

  • This principle was in favor of the wave nature of matter
  • It stated that it is impossible to simultaneously evaluate the precise position and momentum of particle. There is always some probability in predicting the position and momentum of a particle. Mathematically, it can be written as:

                   (Δx)(Δp) ≥ h/(2π)

 

Considering the above equation, 2 cases are possible:

  • Case-1- If precise momentum(p) of an electron is known, then its wavelength by De Broglie’s hypothesis will be constant:

              λ = h/p

It means that the wavelength has a fixed value and the wave is extended infinitely throughout the wave. Hence, it is impossible to find the position of the wave.

Mathematically, if   p = fixed  , Then, Δp→0, Δx→∞

  • Case-2- If the wave is localized, having finite end points

A localized wave is shown below:

As we can see in the diagram, the wavelength (λ) is not fixed, so the momentum (p) is also not fixed.

Hence, there is uncertainty in both, momentum (p) and position (x).

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