The Uncertainty Principle

THE UNCERTAINTY PRINCIPLE

The position and the velocity of the bodies which we come across in our daily life can be determined accurately at a particular instant of time. Hence the path or trajectories of such bodies can be predicted. However, Werner Heisenberg in 1927 pointed out that we can never measure simultaneously and accurately both the position and velocity (or momentum) of a microscopic particle as small as an electron. Thus, it is not possible to talk of trajectory of an electron. This principle, which is a direct consequence of the dual nature of matter and radiation, states that, 'it is impossible to measure simultaneously both the position

and velocity (or momentum) of a microscopic particle with absolute accuracy or certainty.'

Mathematically, uncertainty principle can be put as follows.

Del x. Del  >= h/ 4pi

where, Del x = uncertainity in the position of the particle and

Del p = uncertainity in the momentum of the particle.

The sign >= means that the product of Del x and Del p can be either greater than or equal to h/4pi but can never be less than h/4pi.

Example 1

Calculate the uncertainty in the velocity of a wagon of mass 3000kg

whose position is known to an accuracy of ± 10 pm (Planck's constant = 6.626 × 10⁻³⁴ Kg m² s^-1.

Solution :   Here we are given

m        = 3000 kg x = 10 pm

=  10 ×10^-12 m = 10^-11 m

By uncertainty principle,

Del v = h/ (4pi x m x Delx ) = =  1.76× 10^-27ms^-1