It is not possible to determine preciselt both the position and momentum (or velocity) of a small moving particle such as electron, proton etc. This is known as Heisenber uncertainty principle. The mathemactical form of this principle is :
`Delta x.Delta p ge (h)/(4pi)` (constant)
However this principle is irrevalent in case of bigger particles such as a cup, ball, car etc., that we come across in our daily life.
Given that the mass of electron is `9.1 xx 10^(-31) kg` and velocity of electron is `2.2 xx 10^(6) ms^(-1)`, if uncertainty in its velocity is `0.1%`, the uncertainty in position would be

Options

A. 26 nm
B. 32 nm
C. 48 nm
D. 50 nm

Answer

A

Explanation

`Delta upsilon =(0.1)/(100)xx2.2xx10^(6)=2.2xx10^(3)ms^(-1)`
`Deltax=(h)/(4pimDeltav)`
`=((6.626xx10^(-34)kgm^(2)s^(-1)))/(4.xx3.143xx(9.1xx10^(-31)kg)xx(2.2xx10^(3)ms^(-1)))`
`=0.0263xx10^(-6)m`
`=26.3xx10^(-9)m=26.3 nm`.