A dust particle has mass equal to `10^(-11)g` , diameter equal to `10^(-4)` cm and velocity equal to`10^(-4) cms^(-1)`. The error in the measurment of velocity is `0.1%` . Calculate the uncertiainty in its position. Comment on the result

Explanation

` u = 10 ^(-4) "cm sec"^(-1)`
` :. Delta u = ( 0. 1 xx 10^(-4))/(100) = 1xx 10^(-7) cm sec^(-1)`
Now ,` Delta u . Delta x = h/( 4 pi m)`
` :. Delta x = ( 6.626 xx 10^(-27))/( 4 xx 3. 14 xx 10^(-11) xx 10^(-7))`
`=0.527 xx 10^(-9)` cm
The uncertainty in position as compared to particle
` = (Deltax )/( diameter )`
` = ( 0. 527 xx 10^(-9))/( 10^4) = 0. 527 xx 10^(-5)`
The factor is very small and alost negligible for microscopic particels ,