It is impossible to measure simultaneously the position and momentum of a small particle with absolute accuracy or certainty. If an attempt is made to measure any one of these two quantities with higher accuracy, the other becomes less accurate. The product of the uncertainty in the position (Δx) and the uncertainty in the momentum (Δp = m.Δv where m is the mass of the particle and Δv is the uncertainty in veloity) is alwyas constant and is equal to or greater than h/4π, where h is Plank's constant, that is
Δx.Δp ≥ h/4π ..... (i)
The mathematical expression,
From (i) and (ii), the value of Δp calculated for a given value of Δx is the minimum value for Δp.
Similarly the value of Δp will be the minimum value for Δx.
Putting Δp = m x Δv , eqn. (i) becomes Δx . (mΔv) ≥ h/4π or Δ x . Δv ≥ h / 4πm.
This implies that the position and velocity of a particle cannot be measured simultaneously with certainty.
It is important to understand that uncertainty principle applies to position and momentum along the same axis. Thus if Δx is along X-axis, then Δp should also be along X-axis. It is further important to remember that the uncertainty principle is not on accunt of any limitation of the measuring instrument.