Heisenberg’s uncertainty principle-  given by Warner Heisenberg

“It is impossible to measure simultaneously both the position and momentum of a small particle with absolute accuracy.

If attempt to measure any one of these quantities with higher accuracy, other become less accurate.

The product of uncertainty in the position (Δϸ)  and uncertainty in the momentum (Δx) is always constant and is equal to or greater then h/4π.

∆x * ∆p_x ≥ h/4π

Or        ∆x * ∆(mv_x) ≥ h/4π

Or        ∆x * ∆v_x  ≥ h/4πm

            m = mass of particle

            Δv= uncertainly in velocity 

Thus position and velocity of a particle can’t be measured simultaneously with certainty.

Significance of Heisenberg Uncertainty principle-

Only for the microscopic particles like electron, proton etc. because the product of ∆x and ∆p are quite significant due to this reason, Bohr concept of fixed path with definite position and momentum of the electron have been replaced by stating that the electron has the probability of having a given position and momentum.

Heisenberg uncertainty principle in our daily life.

 No significance in our daily life because we came across only large object. The position and velocity of these objects cases and be defer missed accurately because in these cases, the charges that occur due to impact of light are negligible.

Why electron can’t exist in the Nucleus?

Diameter of the at nucleus = 10^-15m

If electron were exist within the nucleus then max Δx =10^-15m

Mass of e = 9.1 x 10^-31kg

Maximum uncertainly in velocity =?

5.77 x 10-10  m/s       This value is much higher than the velocity of light  (3 x108 m/s ). Hence e- can’t existing nucleus.

Failure of Bohr model – according to Bohr model electrons are moving in fixed circular path, but according to the uncertainty principle, path can be defined only it the velocity and position of the electron are known exactly at the same time, similarly Bohr model does not take wave mature of electron into consideration.