38) h = 6.63 x 10-34 J•s me = 9.11 x 10-28 g v = (3.00 ± 0.01) x 105 m/s
(a) x >= h/4*3.14*m*v
x
>= 6.63 x 10-34 J•s/4 * 3.14 * 9.11 x 10-28
g * 1 kg/103 g * 1.0 x 103 m/s
= 6 x 10-8 m
(b)
x >= 6.63 x 10-34 J•s/4 * 3.14
* 1.67 x 10-24 g * 1 kg/103 g * 1.0
x 103 m/s = 3 x 10-11 m
(c) For particles moving with the same uncertainty in their velocity, the more massive particles have a smaller uncertainty in their position. In our present day model of the atom, we know where the more massive particles (i.e. neutrons) are located but according to the Heisenberg's uncertainty principle, if we know the speed of an electron, we can not know the location of the electron with any certainty.