Calculate the uncertainty in the position of a dust particle with mass equal to 1 mg if uncertainty in its velocity is `5.5 xx 10 ^(-20) ms ^(-1).`

Explanation

We are given that
Mass of dust particle = 1 mg
Uncertainty in velocity `=5.5 xx 10 ^(-20) ms ^(-1)`
We are to find out uncertainty in the position of a dust particle.
We know that
According to Heisenberg uncertainty principle
`Delta x . Delta p = (h)/( 4pi)`
`Delta x = ( h)/( 4 pi Delta p ) = (6.626 xx 10 ^( - 34) )/( 4 xx 3. 14 xx 14 xx 1 xx 10 ^(-3) xx 5.5 xx 10 ^(-20))`
`Delta x = 9. 58 xx 10 ^(-10) m.`
So, the uncertainty in the position is `9. 58 xx 10 ^(-10) m.`