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.

**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 m^{2} 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 ^{-27}ms^{-1}**

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