So far, we have been believing that anything can be specified to any desired degree of accuracy. However, Heisenberg in 1927, put forward a principle known as Heisenberg uncertainity principle. It states that.
“It is not possible to measure simultaneously both the position and momentum (or velocity) of a microscopic particle, with absolute accuracy”. Mathematically, this law may be expressed as :
$\vartriangle x$ x $\vartriangle p$ = h/4$\pi $
$\vartriangle x$ = uncertainity in position
$\vartriangle p$ = uncertainity in momentum The sign $\ge $ means that the product of $\vartriangle x$ and $\vartriangle p$ can be either greater than or equal to h/4$\pi $ lt can never be less than h/4$\pi $. The sign of equality refers to minimum uncertainity and is equal to h/4$\pi $
The constancy of the product of uncertainities means that :
• If $\vartriangle x$ is small i.e., the position of the particle is measured accurately, $\vartriangle p$ would be large, i.e., there would be large uncertainity in its momentum.
On the other hand, if $\vartriangle p$ is small, the momentum of the particle is measured more accurately. $\vartriangle x$ would be large i.e., there would be large uncertainity with regard to the position of the particle.
In other words, if the position of a particle is measured accurately, there will be more error in the measurement of momentum. Conversely, if momentum is measured more accurately the position will not be accurately known.
Since momentum p = mv, therefore
$\vartriangle p$ = m$\vartriangle v$ because mass is constant. The above relation may also be written as
$\vartriangle p$ x m ( $\vartriangle v$) = h/4$\pi $
$\vartriangle x$ x $\vartriangle v$ = h/4$\pi $m
This also means that the position and velocity of an object cannot be simultaneously known with