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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 |
Answer» ` 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 , |
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