A small dust particle of mass 790 x 106 g is being observed

A small dust particle of mass 7.90 x 10^-6 g is being observed under a magnifying lens. Its position is determined to within 0.0050 mm. (1 y = 3.156 x 10^7 s ,h = 6.626 x 10^-34 J . s)

a) Find the minimum uncertainty in its velocity implied by the uncertainty in its position. Ans = 4.6*10^-21m/s show work

b) Assuming the dust particle is moving at the speed you just found, how many years would it take for the particle to move 1.0 mm? 6.9*10^9 yrs show work

Solution

(A) Using uncertainity principal.

deltax. deltap = h / 2pi

(0.0050 x 10^-3) ( 7.90 x 10^-9 x v ) = (6.626 x 10^-34)/(2pi)

v = 2.67 x 10^-21 m/s

(B) d = vt

t = (1 x 10^-3 m ) / (2.67 x 10^-21 m/s)

t = 3.746 x 10^17 sec

t (in yrs) = 3.746 x 10^17 / (3.156 x 10^7)

      = 1.187 x 10^10 yrs