Heisenberg uncertainty principle

It states that, “It is impossible to determine both the position and 
momentum of electron simultaneously with greater accuracy.”

This is simply because;-
(i)The size of an electron is very small such that radiation of high energy with extremely small wavelength are required to detect it.
(ii) Impact of these high energy photons changes both the direction and speed of the electron. 
Thus; the very act of measurement disturbs the position of electron. As the result the uncertainties in  determination of these two quantities vary inversely.
i.e. If one is determined fairly accurately, the other must be corresponding less accurate.
The distance of electron: Is a position of electron from the nucleus and momentum of electrons is product of mass of 
electrons and velocity of the electron.

Heisenberg put forward an expression which is used to determine uncertainty position and momentum of electrons.
Where: P – uncertainty due to momentum
X – Uncertainty due to position.

 p∝1
      ∆X

 p ∝[ h ]× 1
         4π    ∆X
 p∝    h  
       4π∆X  ..................(i)
since; h is a
          4π
proportionality constant.

 ⇒c =   h 
         4π∆X ..................(ii)

Problem # 08
The uncertainty in the momentum of particles is 3.3 x 10^-16gms-¹. Find accuracy with which its
position can be determined.

solution
Given
Uncertainty due to momentum, p =3.3×10^-16gms-¹.
Required accuracy in postion, ∆X.

Recall; p =   h 
                  4π∆X
 ⇒∆X =   h  
             4πp
     =      6.63×10-³⁴Js
      4×π×3.3×10^-16gms-¹
 .: Accuracy in position, ∆X = 1.60×10^-16m

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