If an electron's position can be measured to an accuracy of 3.7*10-8 m, how accurately can its speed be known

Answer 1

The electron position is easier to know bcs they r moving to lines.But they're moving very fast and the scientist don't know their speed yet.Nice question.

Answer 2

Heisenberg's Uncertainty 1/2 h-bar <= delx delp specifies that the more precise we locate (x) its position the more widespread is momentum (p) becomes...and vice versa. And the spread (del) of the two factors will be greater than or equal to 1/2 h-bar, where h is the Plank constant and h-bar = h/2pi.

Momentum = mv = p; so given m is fixed for an electron, delp = m delv and the spread (uncertainty) of the velocity is delp/m = delv. Thus, we have 1/2h-bar >= delx delp = delx delv/m; if your "accuracy" means delx = 3.7 X 10^-8 m, then the speed (v) can be known to 1/2 h-bar m/delx >= delv. You can look up the h and electron mass to solve for delv. The >= in the relationship means the delv answer (the speed accuracy) will be no smaller than that value...it could be bigger.