Heisenberg's uncertainity 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/pIt 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
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).